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NATURAL  INHERITANCE 


9- 


NATURAL  INHERITANCE 


BY 


FRANCIS  GALTON,  F.R.S. 


^ 


AUTHOR   OF 
"  HEREDITARY   GENIUS,"    "  INQUIRIES    INTO    HUMAN   FACULTY,"    ETC. 


CHESTNUT  liiLL,AIAS& 


MACMILLAN    AND    CO. 

AND    LONDON 

1894 


ITm,  Right  of  Translation  and  Beprodiiction  is  Reserved 

BOSTON   OOLLi^vTi^  ..,.x  •.>..' ^ 
CHKST.NIJT  BILL,  MASb. 


Kkhard  Clav  and  Sons,  Limitkd, 

LONDON    AND   BfNGAY. 


65941 


CONTENTS. 


CHAPTER   I. 


Introductoky 


CHAPTER  II. 


Processes  in  Heredity 


Natural  and  Acquired  Peculiarities,  4. — Transmutation  of  Female 
into  Male  measures,  5. — Particulate  Inheritance,  7. — Family 
Likeness  and  Individual  Variation,  9. — Latent  Characteristics, 
11. — Heritages  that  Blend,  and  those  that  are  mutually  Ex- 
clusive, 12. — Inheritance  of  Acquired  Faculties,  14.— Variety 
of  Petty  Influences,  16. 

CHAPTER  III. 

Organic  Stability 18 

Incipient  Structure,  18. — Filial  Relation,  19. — Stable  Forms  20. — 
Subordinate  Positions  of  Stability,  25. — Model,  27. — Stability 
of  Sports,  30.— Infertility  of  Mixed  Types,  31.— Evolution 
not  by  Minute  Steps  only,  32. 

CHAPTER  IV. 

Schemes  of  Distribution  and  op  Frequency 35 

Fraternities  and  Populations  to  be  treated  as  units,  35. — Schemes 
of  Distribution  and  their  Grades,  37. — The  Shape  of  Schemes 
is  independent  of  the  number  of  Observations,  44. — Data  for 
eighteen  Schemes,  46. — Application  of  Schemes  to  inexact 
measures,  47. — Schemes  of  Frequency,  49. 


vi  CONTENTS. 

CHAPTER  V. 

PAGE 

Normal  Variability 51 

Scheme  of  Deviations,  51. — Normal  Curve  of  Distributions,  54. — 
Comparison  of  the  Observed  with  the  Normal  Curve,  56.— The 
value  of  a  single  Deviation  at  a  known  Grade,  determines  a 
Normal  Scheme  of  Deviations,  60.— Two  Measures  at  known 
Grades,  determine  a  Normal  Scheme  of  Measures,  61.  The 
Charms  of  Statistics,  62. — Mechanical  Illustration  of  the  Cause 
of  Curve  of  Frequency,  63.— Order  in  Apparent  Chaos,  66. — 
Problems  in  the  Law  of  Error,  66. 

CHAPTER  VI. 
Data "71 

Records  of  Family  Faculties,  or  R.F.F.  data,  72.— Special  Data, 
78. — Measures  at  my  Anthropometric  Laboratory,  79. — Experi- 
ments in  Sweet  Peas,  79. 

CHAPTER   VII. 

Discussion  of  the  Data  of  Stature 83 

Stature  as  a  Subject  for  Inquiry,  83. — Marriage  Selection,  85. — 
Issue  of  Unlike  Parents,  88, — Description  of  the  Tables  of 
Stature,  91. — Mid-Stature  of  the  Population,  92. — Variability 
of  the  Population,  93.' — Variability  of  Mid-Parents,  93, — 
Variability  in  Co-Fraternities,  94. — Regression, — a,  Filial,  95  ; 
&,  Mid- Parental,  99  ;  c,  Parental,  100  ;  d,  Fraternal,  108.— 
Squadron  of  Statures,  110, — Successive  Generations  of  a 
People,  115. — Natural  Selection,  119. — Variability  in  Frater- 
nities :  First  Method,  124  ;  Second  Method,  127 ;  Third 
Method,  127  ;  Fouith  Method,  128  ;  Trustworthiness  of  the 
Constants,  130  ;  General  view  of  Kinship,  132. — Separate  Con- 
tribution of  each  Ancestor,  134. — Pedigree  Moths,  136. 

CHAPTER   VIII. 

Discussion  of  the  Data  of  Eye  Colour 138 

Preliminary  Remarks,  138, — Data,  139.— Persistence  of  Eye 
Colour  in  the  Population,  140. — Fundamental  E3'-e  Colours, 
142. — Principles  of  Calculation,  148. — Results,  152. 


CONTENTS.  vii 


CHAPTER  IX. 

PAGE 

The  Artistic  Faculty 154 

Data,  154. — Sexual  Distribution,  156.—  Marriage  Selection,  157. — 
Regression,  158.  — Effect  of  Bias  in  Marriage,  162. 


CHAPTER  X. 

Disease 164 

Preliminary  Problem,  165. — Data,  167. — Trustwortbiness  of 
R.F.F.  data,  167. — Mixture  of  Inberitances,  167. — Consump- 
tion :  General  remarks,  171  ;  Distribution  of  Fraternities, 
174  ;  Severely  Tainted  Fraternities,  176  ;  Consumptivity,  181. 
— Data  for  Hereditary  Diseases,  185. 

CHAPTER  XI. 

Latent  Elements 187 

Latent  Elements  not  very  numerous,  187  ;  Pure  Breed,  189. — 
Simplification  of  Hereditary  Inquiry,  190. 

CHAPTER   XII. 
Summary ,    .    .    . 192 


viii  CONTENTS. 


TABLES. 

The  words  by  which  the  various  Tables  are  here  described,  have  been 
chosen  for  the  sake  of  qnick  reference  ;  they  are  often  not  identical  with 
those  used  in  their  actual  headings. 

No.  of  the  Subjects  OF  THE  Tables.  '  page 

i  abies. 

1.  Strengths  of  Pull  arranged  for  drawing  a  Scheme 199 

2.  Data  for  Schemes  of  Distribution  for  various  Qualities  and 

Faculties 200 

3.  Evidences  of  the  general  applicability  of  the  Law  of  Frequency 

of  Error 201 

4.  Values  for  the  Normal  Curve  of  Frequency  (extracted  from 

the  well-known  Table) 202 

5.  Values  of  the  Probability  Integral   (extracted  from  the  well- 

known  Table)   .    .    .    ." 202 

6.  A^alues  of  the  Probability  Integral  when  the  scale  by  which 

the  Errors  are  measured  has  the  Prob  :  Error  for  its  Unit  .    203 

7.  Ordinates  to  the  Normal  Curve  of  Distribution,  when  its  100 

Grades  run  from  -  50°,  through  0°,  to  -f  50^ 204 

8.  Ditto  when  the  Grades  run  from  0°  to  lOO"".     {This  Table  is 

espeiially  adapted  for  use  with  Schemes) 205 

9.  Marriage  Selection  in  respect  to  Stature 206 

9a.     Marriage  Selection  in  respect  to  Eye  Colour 206 

9Z),     Marriages  of  the  Artistic  and  the  Non  Artistic 207 

10.  Issue  of  Parents  who  are  unlike  in  Stature 207 

11.  Statures  of  adult  children  born  to  Mid   Parents   of  Various 

Statures 208 

1 2.  Statures  of   the   Brothers   of  men   of  various  Statures,  fi'om 

P.F.F.  data 209 


CONTENTS.  ix 

Tables  ^"^                                           Subjects  of  the  Tables.  page 

13.  Ditto  from  the  Special  data 210 

14.  Deviations  of  Individual  brothers  from  their  common  Mid- 

Fraternal  Stature 211 

15.  Frequency  of  the  different  Eye  Colours  in  4  successive  Gene- 

rations     212 

16.  The  Descent  of  Hazel-Eyed  families 213 

17.  Calculated  contributions  from  Parents  and  from  Grandparents, 

according  as  they  are  Light,  Hazel,  or  Dark  eyed     .    .    .    .  213 

18.  Examples  of  the  application  of  Table  17 214 

19.  _  Observed  and  calculated  Eye  Colours  in  16  groups  of  families  215 

20.  Ditto  in  78  separate  families 216 

21.  Amounts  of  error  in  the  various  calculations  of  anticipated 

Eye  Colour 218 

22.  Inheritance  of  the  Artistic  Faculty 218 


APPENDICES. 

A.  Memoirs  and  Books  on  Heredity  by  the  Author 219 

B.  Problems  by  J.  D.  Hamilton  Dickson 221 

C.  Experiments  on  Sweet  Peas,  bearing  on  the  law  of  Eegression  .    .  225 

D.  Good  and  bad  Temper  in  English  Families 226 

E.  The  Geometric  Mean  in  "Vital  and  Social  Statistics  . 238 

F.  Probable  extinction  of  Families,  214  ;  Discussion  of  the  Problem 

by  the  Eev.  H.  W.  Watson,  D.Sc 241 

G.  Orderly  arrangement  of  Hereditary  Data 248 

Index 257 


NATURAL   INHERITANCE 


NATUKAL    INHERITANCE, 


CHAPTEE   L 

INTRODUCTOEY. 

I  HAVE  long  been  engaged  upon  certain  problems  tliat 
lie  at  the  base  of  tlie  science  of  heredity,  and  during 
several  years  have  published  technical  memoirs  concern- 
ing them,  a  list  of  which  is  given  in  Appendix  A. 
This  volume  contains  the  more  important  of  the  results, 
set  forth  in  an  orderly  way,  w^ith  more  completeness 
than  has  hitherto  been  possible,  together  with  a  large 
amount  of  new  matter. 

The  inquiry  relates  to  the  inheritance  of  moderately 
exceptional  qualities  by  brotherhoods  and  multitudes 
rather  than  by  individuals,  and  it  is  carried  on  by 
more  refined  and  searching  methods  than  those  usually 
employed  in  hereditary  inquiries. 

One  of  the  problems  to  be  dealt  with  refers  to  the 
curious  regularity  commonly  observed  in  the  statistical 
peculiarities  of  great  populations  during  a  long  series  of 

B 


2  NATURAL  INHEHITANCE.  [chap. 

generations.  The  large  do  not  always  begefc  the  large, 
nor  the  small  the  small,  and  yet  the  observed  propor- 
tions between  the  large  and  the  small  in  each  degree  of 
size  and  in  every  quality,  hardly  varies  from  one  gener- 
ation to  another. 

A  second  problem  regards  the  average  share  con- 
tributed to  the  personal  features  of  the  offspring  by  each 
ancestor  severally.  Though  one  half  of  every  child 
may  be  said  to  be  derived  from  either  parent,  yet  he 
may  receive  a  heritage  from  a  distant  progenitor  that 
neither  of  his  parents  possessed  as  personal  character- 
istics. Therefore  the  child  does  not  on  the  average 
receive  so  much  as  one  half  of  his  personal  qualities 
from  each  parent,  but  something  less  than  a  half.  The 
question  I  have  to  solve,  in  a  reasonable  and  not  merely 
in  a  statistical  way,  is,  how  much  less  ? 

The  last  of  the  problems  that  I  need  mention  now, 
concerns  the  nearness  of  kinship  in  different  degrees. 
We  are  all  ag;reed  that  a  brother  is  nearer  akin  than  a 
nephew,  and  a  nephew  than  a  cousin,  and  so  on,  but 
how  much  nearer  are  they  in  the  precise  language  of 
numerical  statement  ? 

These  and  many  other  problems  are  all  fundamentally 
connected,  and  I  have  worked  them  out  to  a  first  degree 
of  approximation,  with  some  completeness.  The  con- 
clusions cannot  however  be  intelligibly  presented  in 
an  introductory  chapter.  They  depend  on  ideas  that 
must  first  be  well  comprehended,  and  which  are  now 
novel  to  the  large  majority  of  readers  and  unfamiliar 
to  all.     But  those  who   care  to  brace  themselves  to  a 


I.]  INTRODUCTORY.  3 

sustained  effort,  need  not  feel  much  regret  that  the 
road  to  be  travelled  over  is  indirect,  and  does  not 
admit  of  being  ma^pped  beforehand  in  a  way  they  can 
clearly  understand.  It  is  full  of  interest  of  its  own. 
It  familiarizes  us  with  the  measurement  of  variability, 
and  with  curious  laws  of  chance  that  apply  to  a  vast 
diversity  of  social  subjects.  This  part  of  the  inquiry 
may  be  said  to  run  along  a  road  on  a  high  level, 
that  affords  wide  views  in  unexpected  directions,  and 
from  w^hich  easy  descents  may  be  made  to  totally 
different  goals  to  those  we  have  now  to  reach.  I  have 
a  great  subject  to  write  upon,  but  feel  keenly  my 
literary  incapacity  to  make  it  easily  intelligible  without 
sacrificing  accuracy  and  thoroughness. 


r 


P>  2 


r 


CHAPTEE  11. 

PROCESSES    m    HEREDITY. 

Natural  and  Acquired  Peculiarities. — Transmutation  of  Female  into  Male 
Measures. — Particulate  Inheritance. — Family  Likeness  and  Individual 
Variation. — Latent  Characteristics. — Heritages  tliat  Blend  and  those 
that  are  Mutually  Exclusive. — Inheritance  of  Acquired  Faculties. — 
Variety  of  Petty  Influences. 

A  CONCISE  account  of  the  cliief  processes  in  heredity 
will  be  given  in  this  chapter,  partly  to  serve  as  a 
reminder  to  those  to  whom  the  works  of  Darwdn  especi- 
ally, and  of  other  writers  on  the  subject,  are  not 
familiar,  but  principally  for  the  sake  of  presenting  them 
under  an  aspect  that  best  justifies  the  methods  of 
investigation  about  to  be  employed. 

Natural  and  Acquired  Peculiarities. — The  peculiari- 
ties of  men  may  be  roughly  sorted  into  those  that 
are  natural  and  those  that  are  acquired.  It  is  of  the 
former  that  I  am  about  to  s|)eak  in  this  book.  They 
are  noticeable  in  every  direction,  but  are  nowhere  so 
remarkable  as  in  those  twins  ^  who  have  been  dissimilar 

1  See  Human  Faculty,  237. 


CHAP.  II.]  PROCESSES   IN   HEIIEDITY.         .  5 

in  features  and  disposition  from  tlieir  earliest  years, 
thongli  brouo^lit  into  tlie  world  under  the  same  condi- 
tions  and  subsequently  nurtured  in  an  almost  identical 
manner.  It  may  be  that  some  natural  peculiarity  does 
not  appear  till  late  in  life,  and  yet  may  justly  deserve 
to  be  considered  natural,  for  if  it  is  decidedly  exceptional 
in  its  character  its  origin  could  hardly  be  ascribed  to 
the  effects  of  nurture.  If  it  was  also  possessed  by  some 
ancestor,  it  must  be  considered  to  be  hereditary  as 
well.  But  "Natural"  is  an  unfortunate  word  for 
our  purpose ;  it  implies  that  the  moment  of  birth  is 
the  earliest  date  from  which  the  effects  of  surrounding 
conditions  are  to  be  reckoned,  although  nurture  begins 
much  earlier  than  that.  I  therefore  must  ask  that  the 
word  "Natural"  should  not  be  construed  too  literally, 
any  more  than  the  analogous  phrases  of  inborn,  con- 
genital, and  innate.  This  convenient  laxity  of  expres- 
sion for  the  sake  of  avoiding  a  pedantic  periphrase  need 
not  be  accompanied  by  any  laxity  of  idea. 

Transmutation  of  Female  into  Male  Measures. — We 
shall  have  to  deal  with  the  hereditary  influence  of  parents 
over  their  offspring,  although  the  characteristics  of  the 
two  sexes  are  so  different  that  it  may  seem  impossible 
to  speak  of  both  in  the  same  terms.  The  phrase  of 
"  Average  Stature  "  may  be  applied  to  two  men  without 
fear  of  mistake  in  its  interpretation  ;  neither  can  there 
be  any  mistake  when  it  is  applied  to  two  women,  but 
what  meanino^  can  we  attach  to  the  word  "  Averas^e  " 
w^hen  it  is  applied  to  the  stature  of  two  such   different 


G  NATURAL   INHERITANCE.  [chap. 

beings  as  the  Father  and  the  Mother  ?  How  can  we 
appraise  the  hereditary  contributions  of  different  an- 
cestors whether  in  this  or  in  any  other  quality,  unless 
we  take  into  account  the  sex  of  each  ancestor,  in  addi- 
tion to  his  or  her  characteristics  ?  Again,  the  same 
group  of  progenitors  transmits  qualities  in  different 
measure  to  the  sons  and  to  the  daughters  ;  the  sons 
being  on  the  whole,  by  virtue  of  their  sex,  stronger, 
taller,  hardier,  less  emotional,  and  so  forth,  than  the 
daughters.  A  serious  complexity  due  to  sexual  differ- 
ences seems  to  await  us  at  every  step  when  investigating 
the  problems  of  heredity.  Fortunately  we  are  able  to 
evade  it  altogether  by  using  an  artifice  at  the  outset,  else, 
looking  back  as  I  now  can,  from  the  stage  which  the 
reader  will  reach  when  he  finishes  this  book,  I  hardly 
know  how  we  should  have  succeeded  in  making  a 
fair  start.  The  artifice  is  never  to  deal  with  female 
measures  as  they  are  observed,  but  always  to  employ 
their  male  equivalents  in  the  place  of  them.  I  trans- 
mute all  the  observations  of  females  before  taking 
them  in  hand,  and  thenceforward  am  able  to  deal 
with  them  on  equal  terms  with  the  observed  male 
values.  For  example  :  the  statures  of  women  bear  to 
those  of  men  the  proportion  of  about  twelve  to  thir- 
teen. Consequently  by  adding  to  each  observed  female 
stature  at  the  rate  of  one  inch  for  every  foot,  we  are 
enabled  to  compare  their  statures  so  increased  and  trans- 
muted, with  the  observed  statures  of  males,  on  equal 
terms.  If  the  observed  stature  of  a  woman  is  5  feet, 
it  will  count  by  this  rule  as  5  feet  -\-  5  inches;  if  it  be 


II.]  PROCESSES   IN   HEIIEDITY.  ,  7 

6  feet,   as   6   feet  +  6  inclies  ;  if  5-|  feet,   as   5^  feet  + 
5^  inches  ;  that  is  to  say,  as  5  feet  +   Hi  inches/ 

Simihxiiy  as  regards  sons  and  daughters  ;  whatever 
may  be  observed  or  concluded  concerning  daughters 
will,  if  transmuted,  be  held  true  as  regarding  sons, 
and  whatever  is  said  concerning  sons,  will  if  re- 
transrauted,  be  held  true  for  daughters.  We  shall  see 
further  on  that  it  is  easy  to  apply  this  principle  to 
all  measurable  qualities. 

Particulate  Inheritance. — All  livino^  beino\s  are  indi- 
viduals  in  one  aspect  and  composite  in  another.  They 
are  stable  fabrics  of  an  inconceivably  large  number  of 
cells,  each  of  which  has  in  some  sense  a  separate  life  of 
its  own,  ancl  which  have  been  combined  under  influences 
tliat  are  the  subjects  of  much  speculation,  but  are  as 
yet  little  understood.  We  seem  to  inherit  bit  by  bit, 
this  element  from  one  progenitor  that  from  another, 
under  conditions  that  will  be  more  clearly  expressed  as 
we  proceed,  \vhile  the  several  bits  are  themselves  liable 
to  some  small  change  during  the  process  of  transmission. 
Inheritance  may  therefore  be  described  as  largely  if  not 
wholly  "  particulate,"  and  as  such  it  will  be  treated  in 
these  pages.  Though  this  word  is  good  English  and 
accurately  expresses  its  own  meaning,  the  application 

1  .The  proportion  I  use  is  as  100  to  108  ;  that  is,  I  multiply  every  female 
measure  by  108,  which  is  a  very  easy  operation  to  those  who  possess  that 
most  iisefiil  book  to  statisticians,  Crelle's  Tables  (G.  Reimer,  Berlin,  1875). 
It  gives  the  products  of  all  numbers  under  1000,  each  into  each  ;  so  by 
referring  to  the  column  headed  108  the  transmuted  values  of  the  female 
statures  can  be  read  off  at  once. 


8  NATURAL  INHERITANCE.  [chap. 

now  made  of  it  will  be  better  understood  through  an  illus- 
tration. Thus,  many  of  the  modern  buildings  in  Italy 
are  historically  knovv^n  to  have  been  built  out  of  the 
pillaged  structures  of  older  days.  Here  we  may  observe 
a  column  or  a  lintel  serving  the  same  purpose  for  a 
second  time,  and  perhaps  bearing  an  inscription  that 
testifies  to  its  origin,  while  as  to  the  other  stones,  though 
the  mason  may  have  chipped  them  here  and  there,  and 
altered  their  shapes  a  little,  few,  if  any,  came  direct 
from  the  quarry.  This  simile  gives  a  rude  though  true 
idea  of  the  exact  meaning  of  Particulate  Inheritance, 
namely,  that  each  piece  of  the  new  structure  is  derived 
from  a  corresponding  piece  of  some  older  one,  as  a  lintel 
was  derived  from  a  lintel^  a  column  from  a  column,  a 
piece  of  wall  from  a  piece  of  wall. 

I  will  pursue  this  rough  simile  just  one  step  further, 

which  is  as  much  as   it  will  bear.     Suppose   we  were 

building    a    house    with    seeond-hand    materials    carted 

from  a  dealer's  yard,  we  should  often  find  considerable 

portions   of  the    same    old   houses  to  be  still  grouped 

together.      Materials    derived    from  various    structures 

mio^ht  have  been    moved  and  much    shufiled   together 

in  the  yard,    yet  pieces  from  the  same   source  would 

frequently   remain    in    juxtaposition    and    it   may   be 

entangled     They  would  lie  side  by  side  ready  to  be 

carted  away  at  the    same   time   and   to    be   re-erected 

together  anew.     So  in   the   process  of  transmission  by 

inheritance,   elements  derived  from  the   same   ancestor 

are  apt  to  appear  in   large  groups,  just   as  if  they  had 

clung  together  in  the  pre-embryonic  stage,   as  perliaps 


II.]  PROCESSES   IN   HEREDITY.  9 

they  did.  They  form  what  is  well  expressed  by  the 
word  "  traits,"  traits  of  feature  and  character — that  is  to 
say,  continuous  features  and  not  isolated  points. 

We  appear,  then,  to  be  severally  built  up  out  of  a 
host  of  minute  particles  of  whose  nature  we  know 
nothing,  any  one  of  which  may  be  derived  from  any 
one  progenitor,  but  which  are  usually  transmitted  in 
aggregates,  considerable  groups  being  derived  from 
the  same  progenitor.  It  would  seem  that  while  the 
embryo  is  developing  itself,  the  particles  more  or  less 
qualified  for  each  new  post  wait  as  it  were  in  com- 
petition, to  obtain  it.  Also  that  the  particle  that 
succeeds,  must  owe  its  success  partly  to  accident  of 
position  and  partly  to  being  better  qualified  than  any 
equally  well  placed  competitor  to  gain  a  lodgment. 
Thus  the  step  by  step  development  of  the  embryo 
cannot  fail  to  be  influenced  by  an  incalculable  number 
of  small  and  mostly  unknown  circumstances. 

Family  Likeness  and  Individual  Variation. — Natural 
peculiarities  are  apparently  due  to  two  broadly  difi'erent 
causes,  the  one  is  Family  Likeness  and  the  other  is  In- 
dividual Variation.  They  seem  to  be  fundamentally 
opposed,  and  to  require  independent  discussion,  but  this 
is  not  the  case  altogether,  nor  indeed  in  the  greater  part. 
It  will  soon  be  understood  how  the  conditions  that  pro- 
duce a  general  resemblance  between  the  offspring  and 
their  parents,  must  at  the  same  time  give  rise  to  a  con- 
siderable amount  of  individual  differences.  Therefore  I 
need  not  discuss  Family  Likeness  and  Individual  Varia- 


10  NATURAL   INHERITANCE.  [chap. 

tion  under  separate  lieads,  but  as  different  effects  of  the 
same  underlying  causes. 

The  origin  of  these  and  other  prominent  processes 
in  heredity  is  best  exphiined  by  illustrations.  That 
which  will  be  used  was  suggested  by  those  miniature 
gardens,  self-made  and  self-sown,  that  may  be  seen 
in  crevices  or  other  receptacles  for  drifted  earth,  on 
the  otherwise  bare  faces  of  quarries  and  cliffs.  I  have 
frequently  studied  them  through  an  opera  glass,  and 
have  occasionally  clambered  up  to  compare  more  closely 
their  respective  vegetations.  Let  us  then  suppose  the 
aspect  of  the  vegetation,  not  of  one  of  these  detached 
little  gardens,  but  of  a  particular  island  of  substantial 
size,  to  represent  the  features,  bodily  and  mental,  of 
some  particular  parent.  Imagine  two  such  islands 
floated  far  away  to  a  desolate  sea,  and  anchored 
near  together,  to  represent  the  two  parents.  Next 
imagine  a  number  of  islets,  each  constructed  of  earth 
that  was  wholly  destitute  of  seeds,  to  be  reared  near  to 
them.  Seeds  from  both  of  the  islands  will  gradually 
make  their  way  to  the  islets  through  the  agenc}^  of 
winds,  currents,  and  birds.  Vegetation  will  spring  up, 
and  when  the  islets  are  covered  with  it,  their  several 
aspects  will  represent  the  features  of  the  several  children. 
It  is  almost  impossible  that  the  seeds  could  ever  be 
distributed  equally  among  the  islets,  and  there  must  be 
slight  differences  between  them  in  exposure  and  other 
conditions,  corresponding  to  differences  in  pre-natal 
circumstances.  All  of  these  would  have  some  influence 
upon    the   vegetation ;  hence   there    would  be  a  corre- 


II.]  PROCESSES   IN   HEREDITY.  11 

spoiiding  variety  in  the  results.  In  some  islets  one 
plant  would  prevail,  in  others  another ;  nevertheless 
there  would  be  many  traits  of  family  likeness  in  the 
vegetation  of  all  of  them,  and  no  plant  would  be  found 
that  had  not  existed  in  one  or  other  of  the  islands. 

Though  family  likeness  and  individual  variations  are 
largely  due  to  a  common  cause,  some  variations  are  so 
large  and  otherwise  remarkable,  that  they  seem  to 
belong  to  a  different  class.  They  are  known  among 
breeders  as  "  sports  "  ;  I  will  speak  of  these  later  on. 

Latent  Characteristics. — Another  fact  in  heredity 
may  also  be  illustrated  by  the  islands  and  islets  ; 
namely,  that  the  child  often  resembles  an  ancestor  in 
some  feature  or  character  that  neither  of  his  parents 
personally  possessed.  AVe  are  told  that  buried  seeds 
may  lie  dormant  for  many  years,  so  that  when  a 
plot  of  ground  that  was  formerly  cultivated  is  again 
deeply  dug  into  and  upturned,  plants  that  had  not  been 
known  to  grow  on  the  spot  within  the  memory  of  man, 
will  frequently  make  their  appearance.  It  is  easy  to 
imagine  that  some  of  these  dormant  seeds  should  find 
their  way  to  an  islet,  through  currents  that  undermined 
the  island  cliffs  and  drifted  away  their  dehris,  after  the 
cliffs  had  tumbled  into  the  sea.  x\gain,  many  plants  on 
the  islands  may  maintain  an  obscure  existence,  being 
hidden  and  half  smothered  by  successful  rivals  ;  but 
whenever  their  seeds  happened  to  find  their  way  to  any 
one  of  the  islets,  while  those  of  their  rivals  did  not, 
they  would  sprout  freely  and  assert  themselves.     This 


12  NATURAL  INHERITANCE.  [chap. 

illustration  partly  covers  the  analogous  fact  of  diseases 
and  otlier  inheritances  skipping  a  generation,  which  by 
the  way  I  find  to  be  by  no  means  so  usual  an  occurrence 
as  seems  popularly  to  be  imagined. 

Heritages  that  Blend  and  those  that  are  Mutually 
Exclusive. — As  regards  heritages  that  blend  in  the 
offspring,  let  us  take  the  case  of  human  skin  colour. 
The  children  of  the  white  and  the  negro  are  of  a 
blended  tint  ;  they  are  neither  wholly  white  nor 
wdioUy  black,  neither  are  they  piebald,  but  of  a  fairly 
uniform  mulatto  brown.  The  quadroon  child  of  the 
mulatto  and  the  w^hite  has  a  quarter  tint ;  some  of 
the  children  ma}'  be  altogether  darker  or  lighter  than 
the  rest,  but  they  are  not  j)iebald.  Skin-colour  is 
therefore  a  good  example  of  wdiat  I  call  blended  in- 
heritance. It  need  be  none  the  less  ''  particulate " 
in  its  origin,  but  the  result  may  be  regarded  as  a  fine 
mosaic  too  minute  for  its  elements  to  be  distinguished 
in  a  oreneral  view. 

Next  as  regards  heritages  that  come  altogether  from 
one  progenitor  to  the  exclusion  of  the  rest.  Eye-colour 
is  a  fairly  good  illustration  of  this,  the  children  of  a 
light- eyed  and  of  a  dark-eyed  parent  being  much  more 
apt  to  take  their  eye-colours  after  the  one  or  the  other 
than  to  have  intermediate  and  blended  tints. 

There  are  probably  no  heritages  that  perfectly  blend 
or  that  absolutely  exclude  one  another,  but  all  heritages 
have  a  tendency  in  one  or  the  other  direction,  and  the 
tendency  is  often  a  very  strong  one.     This  is  paralleled 


II.]  PROCESSES   IN   HEREDITY.  13 

by  what  we  may  see  in  plots  of  w^ild  vegetation,  where 
two  varieties  of  a  plant  mix  freely,  and  the  general 
aspect  of  the  vegetation  becomes  a  blend  of  the  two, 
or  where  individuals  of  one  variety  congregate  and  take 
exclusive  possession  of  one  place,  and  those  of  another 
variety  congregate  in  another. 

A  peculiar  interest  attaches  itself  to  mutually  exclu- 
sive heritages,  owing  to  the  aid  they  must  afford  to  the 
establishment  of  incipient  races.  A  solitary  peculiarity 
that  blended  freely  with  the  characteristics  of  the  parent 
stock,  would  disappear  in  hereditary  transmission,  as 
quickly  as  the  white  tint  imported  by  a  solitary  Euro- 
pean would  disappear  in  a  black  population.  If  the 
European  mated  at  all,  his  spouse  must  be  black,  and 
therefore  in  the  very  first  generation  the  offspring 
would  be  mulattoes,  and  half  of  his  whiteness  would 
be  lost  to  them.  If  these  mulattoes  did  not  inter- 
breed, the  whiteness  would  be  reduced  in  the  second 
generation  to  one  quarter  ;  in  a  very  few  more  genera- 
tions all  recognizable  trace  of  it  would  have  gone. 
But  if  the  whiteness  refused  to  blend  with  the  black- 
ness, some  of  the  offspring  of  the  wdiite  man  would  be 
wholly  white  and  the  rest  wholly  black.  The  same 
event  would  occur  in  the  grandchildren,  mostly  but 
not  exclusively  in  the  children  of  the  white  offspring, 
and  so  on  in  subsequent  generations.  Therefore, 
unless  the  white  stock  became  wholly  extinct,  some 
undiluted  specimens  of  it  w^ould  make  their  appear- 
ance during  an  indefinite  time,  giving  it  repeated 
r 


14  NATURAL  INHEHITANCE.  [chap. 

cliaiices  of  holding  its  own  in  tlie  struggle  for  existence, 
and  of  establishing  itself  if  its  qualities  were  superior 
to  those  of  the  black  stock  under  any  one  of  manj 
different  conditions. 

Inheritance  of  Acquired  Faculties. — I  am  unpre- 
pared to  say  more  than  a  few  words  on  the  obscure, 
unsettled,  and  much  discussed  subject  of  the  possibility 
of  transmitting  acquired  faculties.  The  main  evidence 
in  its  favour  is  the  gradual  change  of  the  instincts  of 
races  at  large,  in  conformity  with  changed  habits,  and 
through  their  increased  adaptation  to  their  surroundings, 
otherwise  apparently  than  through  the  influence  of 
Natural  Selection.  There  is  very  little  direct  evidence 
of  its  influence  in  the  course  of  a  single  generation,  if 
the  phrase  of  Accjuired  Faculties  is  used  in  perfect 
strictness  and  all  inheritance  is  excluded  that  could  bo 
referred  to  some  form  of  Natural  Selection,  or  of 
Infection  before  birth,  or  of  peculiarities  of  Nurture 
and  Eearing.  Moreover,  a  large  deduction  from  the 
collection  of  rare  cases  must  be  made  on  the  ground 
of  their  being  accidental  coincidences.  When  this 
is  done,  the  remaining  instances  of  acquired  disease 
or  faculty,  or  of  any  mutilation  being  transmitted  from 
parent  to  child,  are  very  few.  Some  apparent  evidence 
of  a  j)ositive  kind,  that  was  formerly  relied  upon,  has 
been  since  found  capable  of  being  interpreted  in  another 
way,  and  is  no  longer  adduced.  On  the  other  hand  there 
exists  such  a  vast  mass  of  distinctly  negative  evidence, 
that  every  instance  offered  to  prove  the  transmission 


II.]  PROCESSES   IN   HEREDITY.  15 

of  acquired  faculties  requires  to  be  closely  criticized. 
For  example,  a  woman  wlio  was  sober  becomes  a 
drunkard.  Her  children  born  during  the  period  of  her 
sobriety  are  said  to  be.  quite  healthy  ;  her  subsequent  chil- 
dren are  said  to  be  neurotic.  The  objections  to  accepting 
this  as  a  valid  instance  in  point  are  many.  The  woman's 
tissues  must  have  been  drenched  with  alcohol,  and  the 
unborn  infant  alcoholised  during  all  its  existence  in  that 
state.  The  quality  of  the  mother's  milk  would  be  bad. 
The  surroundings  of  a  home  under  the  charge  of  a 
drunken  woman  would  be  prejudicial  to  the  health  of 
a  growing  child.  No  wonder  that  it  became  neurotic. 
Again,  a  large  number  of  diseases  are  conveyed  by 
germs  capable  of  passing  from  the  tissues  of  the 
mother  into  those  of  the  unborn  child  otherwise  than 
through  the  blood.  Moreover  it  must  be  recollected 
that  the  connection  between  the  unborn  child  and  the 
mother  is  hardly  more  intimate  than  that  between  some 
parasites  and  the  animals  on  which  they  live.  Not 
a  single  nerve  has  been  traced  between  them,  not  a 
drop  of  blood  ^  has  been  found  to  pass  from  the  mother 
to  the  child.  The  unborn  child  together  with  the 
growth  to  which  it  is  attached,  and  which  is  afterwards 
thrown  off,  have  their  own  vascular  system  to  them- 
selves, entirely  independent  of  that  of  the  mother. 
If  in  an  anatomical  preparation  the  veins  of  the  mother 
are  injected  with  a  coloured  fluid,  none  of  it  enters  the 
veins  of  the  child ;  conversely,  if  the  veins  of  the  child 

1  See  Lectures  by  William  0.  Priestley,  M.D.  (CluircMll,  London,  1860), 
pp.  50,  52,  55,  59,  and  64. 


16  NATURAL   INHERITANCE.  [chap. 

are  injected,  none  of  the  fluid  enters  those  of  the 
mother.  Again,  not  only  is  the  unborn  child  a  sepa- 
rate animal  from  its  mother,  that  obtains  its  air  and 
nourishment  from  her  purely  through  soakage,  but  its 
constituent  elements  are  of  very  much  less  recent 
growth  than  is  popularly  supposed.  The  ovary  of 
the  mother  is  as  old  as  the  mother  herself;  it  was  well 
developed  in  her  own  embryonic  state.  The  ova  it  con- 
tains in  her  adult  life  were  actually  or  potentially  present 
before  she  was  born,  and  they  grew  as  she  grew.  There 
is  more  reason  to  look  on  them  as  collateral  with  the 
mother,  than  as  parts  of  the  mother.  The  same  may 
be  said  with  little  reservation  concerning  the  male 
elements.  It  is  therefore  extremely  difficult  to  see 
how  acquired  faculties  can  be  inherited  by  the  children. 
It  would  be  less  difficult  to  conceive  of  their  inheritance 
by  the  grandchildren.  Well  devised  experiment  into 
the  limits  of  the  power  of  inheriting  acquired  faculties 
and  mutilations,  whether  in  plants  or  animals,  is  one  of 
the  present  desiderata  in  hereditary  science.  Fortunately 
for  us,  our  ignorance  of  the  subject  will  not  introduce 
any  special  difficulty  in  the  inquiry  on  which  we  are 
now  engaged. 

Variety  of  Petty  Influences.— The  mcalculshle  number 
of  petty  accidents  that  concur  to  produce  variability 
among  brothers,  make  it  impossible  to  predict  the 
exact  cjualities  of  any  individual  from  hereditary  data. 
But  we  may  predict  average  results  with  great  cer- 
tainty, as   will  be  seen   further   on,  and  we   can  also 


II.]  PROCESSES   IN  HEREDITY.  17 

obtain  precise  information  concerning  the  penumbra 
of  uncertainty  that  attaches  itself  to  single  predic- 
tions. It  would  be  premature  to  speak  further  of 
this  at  present ;  what  has  been  said  is  enough  to  give 
a  clue  to  the  chief  motive  of  this  chapter.  Its 
intention  has  been  to  show  the  large  part  that  is  always 
played  by  chance  in  the  course  of  hereditary  transmission , 
and  to  establish  the  importance  of  an  intelligent  use  of 
the  laws  of  chance  and  of  the  statistical  methods  that 
are  based  upon  them,  in  expressing  the  conditions 
under  which  heredity  acts. 

I  may  here  point  out  that,  as  the  processes  of  statis- 
tics are  themselves  processes  of  intimate  blendings,  their 
results  are  the  same,  whether  the  materials  had  been 
partially  blended  or  not,  before  they  were  statistically 
taken  in  hand. 


CHAPTER  III. 

ORGIANIC    STABILITY. 

Incipient  Structure. — Filial  relation. — Stable  Forms. — Subordinate  posi- 
tions of  Stability. — Model. — Stability  of  Sports. — Infertility  of  mixed 
Types. — Evolution  not  by  minute  steps  only. 

Incipient  Structure. — The  total  heritage  of  each  man 
must  include  a  greater  variety  of  material  than  was 
utilised  informing  his  personal  structure.  The  existence 
in  some  latent  form  of  an  unused  portion  is  proved  by 
his  power,  already  alluded  to,  of  transmitting  ancestral 
characters  that  he  did  not  personally  exhibit.  There- 
fore the  organised  structure  of  each  individual  should  be 
viewed  as  the  fulfilment  of  only  one  out  of  an  indefinite 
number  of  mutually  exclusive  possibilities.  His  struc- 
ture is  the  coherent  and  more  or  less  stable  development 
of  what  is  no  more  than  an  imperfect  sample  of  a  large 
variety  of  elements. 

The  precise  conditions  under  which  each  several 
element  or  particle  (whatever  may  be  its  nature)  finds 
its  way  into  the  sample  are,  it  is  needless  to  repeat, 
unknown,  but  we  may  provisionally  classify  them  under 
one  or  other  of  the  following  three  categories,  as  they 


CHAP.  III.]  ORGANIC   STABILITY.  19 

apparently  exhaust  all  reasonable  possibilities  :  first,  that 
in  which  each  element  selects  its  most  suitable  immediate 
neighbourhood,  in  accordance  with  the  guiding  idea  in 
Darwin's  theory  of  Pangenesis  ;  secondly,  that  of  more 
or  less  general  co-ordination  of  the  influences  exerted  on 
each  element,  not  only  by  its  immediate  neighbours,  but 
by  many  or  most  of  the  others  as  well ;  finally,  that  of 
accident  or  chance,  under  which  name  a  group  of  agen- 
cies are  to  be  comprehended,  diverse  in  character 
and  alike  only  in  the  fact  that  their  influence  on  the 
settlement  of  each  particle  was  not  immediately  directed 
towards  that  end.  In  philosophical  language  we  say 
that  such  agencies  are  not  purposive,  or  that  they  are 
not  teleological ;  in  popular  language  they  are  called 
accidents  or  chances. 

Filial  Relation. — A  conviction  that  inheritance  is 
mainly  particulate  and  much  influenced  by  chance, 
greatly  afiects  our  idea  of  kinship  and  makes  us  con- 
sider the  parental  and  filial  relation  to  be  curiously 
circuitous.  It  appears  that  there  is  no  direct  hereditary 
relation  between  the  personal  parents  and  the  personal 
child,  except  perhaps  through  little-known  channels  of 
secondary  importance,  but  that  the  main  line  of 
hereditary  connection  unites  the  sets  of  elements  out 
of  which  the  personal  parents  had  been  evolved  with 
the  set  out  of  which  the  personal  child  was  evolved. 
The  main  line  may  be  rudely  likened  to  the  chain  of  a 
necklace,  and  the  personalities  to  pendants  attached  to 
its   links.      We   are    unable   to  see   the   particles   and 

C  2 


20  NATURAL  INHERITANCE.  [chap. 

watch  their  grouping,  and  we  know  nothing  directly 
about  them,  but  we  may  gain  some  idea  of  the  various 
possible  results  by  noting  the  differences  between  the 
brothers  in  any  large  fraternity  (as  will  be  done  further 
on  with  much  minuteness),  whose  total  heritages  must 
have  been  much  alike,  but  whose  personal  structures 
are  often  very  dissimilar.  This  is  why  it  is  so  im- 
portant in  hereditary  inquiry  to  deal  with  fraternities 
rather  than  with  individuals,  and  with  large  fraternities 
rather  than  small  ones.  We  ought,  for  example,  to 
compare  the  group  containing  both  parents  and  all  the 
uncles  and  aunts,  with  that  containing  all  the  children. 
The  relative  weight  to  be  assigned  to  the  uncles  and 
aunts  is  a  question  of  detail  to  be  discussed  in  its 
proper  place  further  on  (see  Chap.  XL) 

Stable  Forms. — The  changes  in  the  substance  of  the 
newly-fertilised  ova  of  all  animals,  of  which  more  is 
annually  becoming  known,  ^  indicate  segregations  as 
well  as  aggregations,  and  it  is  reasonable  to  suppose 
that  repulsions  concur  with  affinities  in  producing 
them.  We  know  nothing  as  yet  of  the  nature  of 
these  affinities  and  repulsions,  but  we  may  expect  them 
to  act  in  great  numbers  and  on  all  sides  in  a  space 
of  three  dimensions,  just  as  the  personal  likings  and  dis- 

1  A  valuable  memoir  on  the  state  of  our  knowledge  of  these  matters  up 
to  the  end  of  1887  is  published  in  Vol.  XIX.  of  the  Proceedings  of  the 
Philosophical  Society  of  Glasgow,  and  reprinted  under  the  title  of  Tlie 
Modern  Cell  Theory,  and  Theories  as  to  the  Physiological  Basis  of  Heredity^ 
by  Prof.  John  Gray  McKendrick,  M.D.,  F.R.S.,  &c.  (R.  Anderson,  Glasgow, 
1888.) 


III.]  ORGANIC   STABILITY.  21 

likings  of  eaeh  indiyidual  insect  in  a  flying  swarm  may 
be  supposed  to  determine  the  position  that  he  occupies 
in  it.  Every  particle  must  have  many  immediate  neigh- 
bours. Even  a  sphere  surrounded  by  other  spheres  of 
equal  sizes,  like  a  cannon-ball  in  the  middle  of  a  heap, 
when  they  are  piled  in  the  most  compact  form,  is  in 
actual  contact  with  no  less  than  twelve  others.  We  may 
therefore  feel  assured  that  the  particles  which  are  still 
unfixed  must  be  affected  by  very  numerous  influences 
acting  from  all  sides  and  varying  with  slight  changes  of 
place,  and  that  they  may  occupy  many  positions  of  tem- 
porary and  unsteady  equilibrium,  and  be  subject  to 
repeated  unsettlement,  before  they  finally  assume  the 
positions  in  which  they  severally  remain  at  rest. 

The  whimsical  eff'ects  of  chance  in  producing  stable 
results  are  common  enough.  Tangled  strings  variously 
twitched,  soon  get  themselves  into  tight  knots.  Eub- 
bish  thrown  down  a  sink  is  pretty  sure  in  time  to  choke 
the  pipe  ;  no  one  bit  may  be  so  large  as  its  bore,  but 
several  bits  in  their  numerous  chance  encounters  will 
at  length  so  come  into  collision  as  to  wedge  themselves 
into  a  sort  of  arch  across  the  tube,  and  efi'ectually  plug 
it.  Many  years  ago  there  was  a  fall  of  large  stones  from 
the  ruinous  walls  of  Kenilworth  Castle.  Three  of  them, 
if  I  recollect  rightly,  or  possibly  four,  fell  into  a  very 
peculiar  arrangement,  and  bridged  the  interval  between 
the  jambs  of  an  old  window.  There  they  stuck  fast, 
showing  clearly  against  the  sky.  The  oddity  of  the 
structure  attracted  continual  attention,  and  its  stability 
was  much  commented  on.     These  hanging  stones,   as 


22  NATURAL   INHERITANCE.  [chap. 

they  were  called,  remained  quite  firm  for  many  years  ; 
at  length  a  storm  shook  them  down. 

In  every  congregation  of  mutually  reacting  elements, 
some  characteristic  groupings  are  usually  recognised 
that  have  become  familiar  through  their  frequent  re- 
currence and  partial  persistence.  Being  less  evanescent 
than  other  combinations,  they  may  be  regarded  as 
temporarily  Stable  Forms.  No  demonstration  is 
needed  to  show  that  their  number  must  be  greatly 
smaller  than  that  of  all  the  possible  combinations  of 
the  same  elements.  I  will  briefly  give  as  great  a 
diversity  of  instances  as  I  can  think  of,  taken  from 
Grovernments,  Crowds,  Landscapes,  and  even  from 
Cookery,  and  shall  afterwards  draw  some  illustrations 
from  Mechanical  Inventions,  to  illustrate  what  is  meant 
by  characteristic  and  stable  groupings.  From  some 
of  them  it  wiU  also  be  gathered  that  secondary  and 
other  orders  of  stability  exist  besides  the  primary 
ones. 

In  Governments,  the  primary  varieties  of  stable  forms 
are  very  few  in  number,  being  such  as  autocracies,  con- 
stitutional monarchies,  oligarchies,  or  republics.  The 
secondary  forms  are  far  more  numerous  ;  still  it  is  hard 
to  meet  with  an  instance  of  one  that  cannot  be  pretty 
closely  paralleled  by  another.  A  curious  evidence  of 
the  small  variety  of  possible  governments  is  to  be  found 
in  the  constitutions  of  the  governing  bodies  of  the 
Scientific  Societies  of  London  and  the  Provinces,  which 
are  numerous  and  independent.  Their  development 
seems  to  follow  a  single  course  that  has  many  stages. 


III.]  ORGANIC   STABILITY.  23 

and  invariably  tends  to  establish  tbe  following  staff  of 
officers  :  President,  vice-Presidents,  a  Council,  Honorary 
Secretaries,  a  paid  Secretary,  Trustees,  and  a  Treasurer. 
As  Britons  are  not  unfrequently  servile  to  rank,  some 
seek  a  purely  ornamental  Patron  as  well. 

Every  variety  of  Crowd  has  its  own  characteristic 
features.  At  a  national  pageant,  an  evening  party,  a 
race-course,  a  marriage,  or  a  funeral,  the  groupings  in 
each  case  recur  so  habitually  that  it  sometimes  appears 
to  me  as  if  time  had  no  existence,  and  that  the  ceremony 
in  which  I  am  taking  part  is  identical  with  others  at 
which  I  had  been  present  one  year,  ten  years,  twenty 
years,  or  any  other  time  ago. 

The  frequent  combination  of  the  same  features  in 
Landscape  Scenery,  justifies  the  use  of  such  expressions 
as  "  true  to  nature,"  when  applied  to  a  pictorial  com- 
position or  to  the  descriptions  of  a  novel  writer.  The 
experiences  of  travel  in  one  part  of  the  world  may 
curiously  resemble  those  in  another.  Thus  the  military 
expedition  by  boats  up  the  Nile  was  planned  from 
experiences  gained  on  the  Eed  Eiver  of  North  America, 
and  was  carried  out  with,  the  aid  of  Canadian  voyageurs. 
The  snow  mountains  all  over  the  world  present  the 
same  peculiar  difficulties  to  the  climber,  so  that  Swiss 
experiences  and  in  many  cases  Swiss  guides  have  been 
used  for  the  exploration  of  the  Himalayas,  the  Caucasus, 
the  lofty  mountains  of  New  Zealand,  the  Andes,  and 
Greenland.  Whenever  the  general  conditions  of  a 
new  country  resemble  our  own,  we  recognise  character- 
istic and  familiar  features  at  every  turn,  whether  we 


24  NATURAL   INHERITANCE.  [chap. 

are  walking  by  the  brookside,  along  the  seashore,  in 
the  woods,  or  on  the  hills. 

Even  in  Cookery  it  seems  difficult  to  invent  a  new 
and  good  dish,  though  the  current  recipes  are  few,  and 
the  proportions  of  the  flour,  sugar,  butter,  eggs,  &c., 
used  in  making  them  might  be  indefinitely  varied  and 
be  still  eatable.  I  consulted  cookery  books  to  learn  the 
facts  authoritatively,  and  found  the  following  passage  : 
"  I  have  constantly  kept  in  view  the  leading  principles 
of  this  work,  namely,  to  give  in  these  domestic  recipes 
the  most  exact  quantities.  ...  I  maintain  that  one 
cannot  be  too  careful ;  it  is  the  only  way  to  put  an  end 
to  those  approximations  and  doubts  which  will  beset  the 
steps  of  the  inexperienced,  and  which  account  for  so 
many  people  eating  indifierent  meals  at  home."  ^ 

It  is  the  triteness  of  these  experiences  that  makes 
the  most  varied  life  monotonous  after  a  time,  and  many 
old  men  as  well  as  Solomon  have  frequent  occasion  to 
lament  that  there  is  nothing  new  under  the  sun. 

The  object  of  these  diverse  illustrations  is  to  impress 
the  meaning  I  wish  to  convey,  by  the  phrase  of  stable 
forms  or  groupings,  which,  however  uncertain  it  may  be 
in  outline,  is  perfectly  distinct  in  substance. 

Every  one  of  the  meanings  that  have  been  attached 
by  writers  to  the  vague  but  convenient  word  ''  type  "  has 
for  its  central  idea  the  existence  of  a  limited  number 

^  The  Royal  Coohery  Book  By  Jules  GoufF^,  Clief  de  Cuisine  of  the  Paris 
Jockey  Club  ;  translated  by  Alphonse  Gouffe,  Head  Pastry  Cook  to  H.M. 
the  Queen.     Sampson  Low.     1869.     Introduction,  p.  9. 


III.]  ORGANIC   STABILITY.  25 

of  frequently  recurrent  forms.  The  word  etymologically 
compares  these  forms  to  the  identical  medals  that  may 
be  struck  by  one  or  other  of  a  set  of  dies.  The  central 
idea  on  which  the  phrase  "  stable  forms  "  is  based  is  of 
the  same  kind,  while  the  phrase  further  accounts  for 
their  origin,  vaguely  it  may  be,  but  still  significantly, 
by  showing  that  though  we  know  little  or  nothing  of 
details,  the  result  of  organic  groupings  is  analogous  to 
much  that  we  notice  elsewhere  on  every  side. 

Siihordwate  positions  of  Stability. — Of  course  there 
are  different  degrees  of  stability.  If  the  same  structural 
form  recurs  in  successively  descending  generations,  its 
stability  must  be  great,  otherwise  it  could  not  have 
withstood  the  effects  of  the  admixture  of  equal  doses  of 
alien  elements  in  successive  generations.  Such  a  form 
well  deserves  to  be  called  typical.  A  breeder  would 
always  be  able  to  establish  it.  It  tends  of  itself  to 
become  a  new  and  stable  variety  ;  therefore  all  the 
breeder  has  to  attend  to  is  to  give  fair  play  to  its 
tendency,  by  weeding  out  from  among  its  offspring  such 
reversions  to  other  forms  as  may  crop  up  from  time  to 
time,  and  by  preserving  the  breed  from  rival  admixtures 
until  it  has  become  confirmed,  and  adapted  in  every 
minute  particular  to  its  surroundings. 

Personal  Forms  may  be  compared  to  Human  Inven- 
tions, as  these  also  may  be  divided  iuto  types,  sub-types, 
and  deviations  from  them.  Every  important  inven- 
tion is  a  new  type,  and  of  such  a  definite  kind  as  to 
admit  of  clear  verbal  description,  and  so  of  becoming 


26  NATURAL   INHERITANCE.  [chap. 

the  subject  of  patent  rights  ;  at  the  same  time  it  need 
not  be  so  minutely  defined  as  to  exclude  the  possibility 
of  small  improvements  or  of  deviations  from  the  main 
design,  any  of  which  may  be  freely  adopted  by  the  in- 
ventor without  losing  the  protection  of  his  patent.  But 
the  range  of  protection  is  by  no  means  sharply  distinct, 
as  most  inventors  know  to  their  cost.  Some  other  man, 
who  may  or  may  not  be  a  plagiarist,  applies  for  a  sepa- 
rate patent  for  himself,  on  the  ground  that  he  has  intro- 
duced modifications  of  a  fundamental  character  ;  in  other 
words,  that  he  has  created  a  fresh  type.  His  application 
is  opposed,  and  the  question  whether  his  plea  be  valid 
or  not,  becomes  a  subject  for  legal  decision. 

Whenever  a  patent  is  granted  subsidiary  to  another, 
and  lawful  to  be  used  only  by  those  who  have  acquired 
rights  to  w^ork  the  primary  invention,  then  we  should 
rank  the  new  patent  as  a  secondary  and  not  as  a 
primary  type.  Thus  we  see  that  mechanical  inventions 
ofi'er  good  examples  of  types,  sub-types,  and  mere 
deviations. 

The  three  kinds  of  public  carriages  that  characterise 
the  streets  of  London  ;  namely,  omnibuses,  hansoms, 
and  four-wheelers,  are  specific  and  excellent  illustra- 
tions of  what  I  wish  to  express  by  mechanical  types, 
as  distinguished  from  sub -types.  Attempted  improve- 
ments in  each  of  them  are  yearly  seen,  but  none  have  as 
yet  superseded  the  old  familiar  patterns,  which  cannot, 
as  it  thus  far  appears,  be  changed  with  advantage,  taking 
the  circumstances  of  London  as  they  are.  Yet  there 
have  been  numerous  subsidiary  and  patented  contriv- 


III.] 


ORGANIC   STABILITY. 


27 


ances,  each  a  distinct  step  in  the  improvement  of  one 
or  other  of  the  three  primary  types,  and  there  are  or 
may  be  in  each  of  the  three  an  indefinite  number 
of  varieties  in  details,  too  unimportant  to  be  subjects 
of  patent  rights. 

The  broad  classes,  of  primary  or  subordinate  types, 
and  of  mere  deviations  from  them,  are  separated  by  no 
well-defined  frontiers.  Still  the  distinction  is  very  ser- 
viceable, so  much  so  that  the  whole  of  the  laws  of  patent 
and  copyright  depend  upon  it,  and  it  forms  the  only 
foundation  for  the  title  to  a  vast  amount  of  valuable 
property.  Corresponding  forms  of  classification  must 
be  equally  appropriate  to  the  organic  structure  of  all 
living  things. 

Model. — The  distinction  between  primary  and  sub- 
ordinate positions  of  stability  will  be  made  clearer  by  the 


riG.T 


help  of  Fig  1,  which  is  drawn  from  a  model  I  made.  The 
model  has  more  sides,  but  Fig.  1  suffices  for  illustration. 
It  is  a  polygonal  slab  that  can  be  made  to  stand  on  any 
one  of  its  edges  when  set  upon  a  level  table,  and  is 


28  NATURAL  INHERITANCE.  [cbap. 

intended  to  illustrate  tlie  meaning  of  primary  and  sub- 
ordinate stability  in  organic  structures,  although  the 
conditions  of  these  must  be  far  more  complex  than 
anything  we  have  wits  to  imagine.  The  model  and  the 
organic  structure  have  the  cardinal  fact  in  common,  that 
if  either  is  disturbed  without  transgressing  the  range  of 
its  stability,  it  will  tend  to  re-establish  itself,  but  if  the 
range  is  overpassed  it  will  topple  over  into  a  new 
position  ;  also  that  both  of  them  are  more  likely  to 
topple  over  towards  the  position  of  primary  stability, 
than  away  from  it. 

The  ultimate  point  to  be  illustrated  is  this.  Though  a 
long  established  race  habitually  breeds  true  to  its  kind, 
subject  to  small  unstable  deviations,  yet  every  now  and 
then  the  offspring  of  these  deviations  do  not  tend  to 
revert,  but  possess  some  small  stability  of  their  own. 
They  therefore  have  the  character  of  sub-types,  always, 
however,  with  a  reserved  tendency  under  strained  con- 
ditions, to  revert  to  the  earlier  type.  The  model  further 
illustrates  the  fact  that  sometimes  a  sport  may  occur  of 
such  marked  peculiarity  and  stability  as  to  rank  as  a 
new  type,  capable  of  becoming  the  origin  of  a  new  race 
with  very  little  assistance  on  the  part  of  natural  selection. 
Also,  that  a  new  type  may  be  reached  without  any  large 
single  stride,  but  through  a  fortunate  and  rapid  succession 
of  many  small  ones. 

The  model  is  a  polygonal  slab,  the  polygon  being  one 
that  might  have  been  described  within  an  oval,  and  it  is 
so  shaped  as  to  stand  on  any  one  of  its  edges.  When  the 
slab  rests  as  in  Fig.  1,  on  the  edge  A  B,  corresponding  to 


III.]  ORGANIC   STABILITY.  29 

the  shorter  diameter  of  the  oval,  it  stands  in  its  most 
stable  position,  and  in  one  from  which  it  is  equally  diffi- 
cult to  dislodge  it  by  a  tilt  either  forwards  or  backwards. 
So  long  as  it  is  merely  tilted  it  will  fall  back  on  being 
left  alone,  and  its  position  when  merely  tilted  corre- 
sponds to  a  simple  deviation.     But  when  it  is  pushed 
with   sufficient   force,   it  will   tumble    on    to  the    next 
edge,  B  c,  into  a   new  position  of  stability.      It   will 
rest  there,  but  less  securely  than  in  its  first  position ; 
moreover  its  range  of  stability  will  no  longer  be  dis- 
posed symmetrically.    A  comparatively  slight  push  from 
the  front  will  suffice  to  make  it  tumble  back,  a  com- 
paratively heavy  push  from  behind  is  needed  to  make 
it   tumble   forward.       If   it    be   tumbled   over   into    a 
third   position    (not   shown   in   the   Fig.),  the   process 
just  described  may  recur  with  exaggerated  effect,  and 
similarly  for  many  subsequent  ones.     If,  however,  the 
slab   is    at   length  brought   to   rest  on   the   edge   c  d, 
most  nearly  corresponding  to  its  longest  diameter,  the 
next  onward  push,  which  may  be  very  slight,  will  suffice 
to  topple  it  over  into  an  entirely  new  system  of  stability  ; 
in  other  words,  a  ''sport"  comes  suddenly  into   exist- 
ence.    Or  the  figure  might  have  been  drawn  with  its 
longest  diameter  passing  into  a  projecting  spur,  so  that 
a  push  of  extreme  strength  would  be  required  to  topple 
it  entirely  over. 

If  the  first  position,  A  B,  is  taken  to  represent  a  type, 
the  other  portions  will  represent  sub-types.  All  the 
stable  positions  on  the  same  side  of  the  longer  diameter 
are  subordinate  to  the  first  position.     On  whichever  of 


30  NATURAL  INHERITANCE.  [chap. 

of  them  the  polygon  may  stand,  its  principal  tendency 
on  being  seriously  disturbed  will  be  to  fall  back  towards 
the  first  position  ;  yet  each  position  is  stable  within 
certain  limits. 

Consequently  the  model  illustrates  how  the  following 
conditions  may  co- exist :  (1)  Variability  within  narrow 
limits  without  prejudice  to  the  purity  of  the  breed. 
(2)  Partly  stable  sub-types.  (3)  Tendency,  when  much 
disturbed,  to  revert  from  a  sub-type  to  an  earlier  form. 
(4)  Occasional  sports  which  may  give  rise  to  new  types. 

Stability  of  Sports. — Experience  does  not  show  that 
those  wide  varieties  which  are  called  ^'  sports "  are 
unstable.  On  the  contrary,  they  are  often  transmitted 
to  successive  generations  with  curious  persistence. 
Neither  is  there  any  reason  for  expecting  otherwise. 
While  we  can  well  understand  that  a  strained  modi- 
fication of  a  type  would  not  be  so  stable  as  one  that 
approximates  more  nearly  to  the  typical  centre,  the 
variety  may  be  so  wide  that  it  falls  into  difi*erent  condi- 
tions of  stability,  and  ceases  to  be  a  strained  modification 
of  the  original  type. 

The  hansom  cab  was  originally  a  marvellous  novelty. 
In  the  language  of  breeders  it  was  a  sudden  and  re- 
markable "  sport,"  yet  the  suddenness  of  its  appearance 
has  been  no  bar  to  its  unchanging  hold  on  popular 
favour.  It  is  not  a  monstrous  anomaly  of  incongruous 
parts,  and  therefore  unstable,  but  quite  the  contrary. 
Many  other  instances  of  very  novel  and  yet  stable 
inventions    could    be    quoted.       One    of    the    earliest 


III.]  ORGANIC   STABILITY.  31 

electrical  batteries  was  that  wliicli  is  still  known  as  a 
Grove  battery,  being  the  invention  of  Sir  William  Grove. 
Its  principle  was  quite  new  at  the  time,  and  it  continues 
in  use  without  alteration. 

The  persistence  in  inheritance  of  trifling  characteristics, 
such  as  a  mole,  a  white  tuft  of  hair,  or  multiple  fingers, 
has  often  been  remarked.  The  reason  of  it  is,  I  presume, 
that  such  characteristics  have  inconsiderable  influence 
upon  the  general  organic  stability ;  they  are  mere 
excrescences,  that  may  be  associated  with  very  different 
types,  and  are  therefore  inheritable  without  let  or 
hindrance. 

It  seems  to  me  that  stability  of  type,  about  which  we 
as  yet  know  very  little,  must  be  an  important  factor  in 
the  general  theory  of  heredity,  when  the  theory  is 
applied  to  cases  of  high  breeding.  It  will  be  shown 
later  on,  at  what  point  a  separate  allowance  requires 
to  be  made  for  it.  But  in  the  earlier  and  principal 
part  of  the  inquiry,  which  deals  with  the  inheritance  of 
qualities  that  are  only  exceptional  in  a  small  degree,  a 
separate  allowance  does  not  appear  to  be  required. 

Infertility  of  Mixed  Types. — It  is  not  difficult  to  see 
in  a  general  way  why  very  different  types  should  refuse 
to.  coalesce,  and  it  is  scarcely  possible  to  explain  the 
reason  why,  more  clearly  than  by  an  illustration.  Thus 
a  useful  blend  between  a  four-wheeler  and  a  hansom 
would  be  impossible  ;  it  would  have  to  run  on  three 
wheels  and  the  half-way  position  for  the  driver  would 
be  upon  its  roof     A  blend  would  be  equally  impossible 


32  NATURAL   INHERITANCE.  [chap. 

between  an  omnibus  and  a  hansom,   and  it  would  be 
difficult  between  an  omnibus  and  a  four-wheeler. 

Evolution  not  hy  Minute  Steps  Only. — The  theory 
of  Natural  Selection  might  dispense  wdth  a  restriction, 
for  which  it  is  difficult  to  see  either  the  need  or  the 
justification,  namely,  that  the  course  of  evolution  always 
proceeds  by  steps  that  are  severally  minute,  and  that 
become  effective  only  through  accumulation.  That 
the  steps  may  be  small  and  that  they  '}nust  be  small  are 
very  different  views ;  it  is  only  to  the  latter  that  I 
object,  and  only  when  the  indefinite  word  *^  small "  is  used 
in  the  sense  of  "  barely  discernible,"  or  as  small  com- 
pared with  such  large  sports  as  are  known  to  have  been 
the  origins  of  new  races.  An  apparent  ground  for  the 
common  belief  is  founded  on  the  fact  that  whenever 
search  is  made  for  intermediate  forms  between  widely 
divergent  varieties,  whether  they  be  of  plants  or  of 
animals,  of  weapons  or  utensils,  of  customs,  religion  or 
language,  or  of  any  other  product  of  evolution,  a  long 
and  orderly  series  can  usually  be  made  out,  each  member 
of  which  differs  in  an  almost  imperceptible  degree  from 
the  adjacent  specimens.  But  it  does  not  at  all  follow 
because  these  intermediate  forms  have  been  found  to 
exist,  that  they  are  the  very  stages  that  w^ere  passed 
through  in  the  course  of  evolution.  Counter  evidence 
exists  in  abundance,  not  only  of  the  appearance  of  con- 
siderable sports,  but  of  their  remarkable  stability  in 
hereditary  transmission.  Many  of  the  specimens  of 
intermediate  forms  may  have  been  unstable  varieties, 


III.]  ORGANIC   STABILITY.  33 

whose  descendants  had  reverted ;  they  might  be  looked 
upon  as  tentative  and  faltering  steps  taken  along  parallel 
courses  of  evolution,  and  afterwards  retraced.  Affiliation 
from  each  generation  to  the  next  requires  to  be  proved 
before  any  apparent  line  of  descent  can  be  accepted 
as  the  true  one.  The  history  of  inventions  fully  illus- 
trates this  view.  It  is  a  most  common  experience  that 
what  an  inventor  knew  to  be  original,  and  believed  to 
be  new,  had  been  invented  independently  by  others 
many  times  before,  but  had  never  become  established. 
Even  when  it  has  new  features,  the  inventor  usually 
finds,  on  consulting  lists  of  patents,  that  other  inventions 
closely  border  on  his  own.  Yet  we  know  that  inventors 
often  proceed  by  strides,  their  ideas  originating  in  some 
sudden  happy  thought  suggested  by  a  chance  occurrence, 
though  their  crude  ideas  may  have  to  be  laboriously 
worked  out  afterwards.  If,  however,  all  the  varieties  of 
any  machine  that  had  ever  been  invented,  were  collected 
and  arranged  in  a  Museum  in  the  apparent  order  of 
their  Evolution,  each  would  differ  so  little  from  its 
neighbour  as  to  suggest  the  fallacious  inference  that  the 
successive  inventors  of  that  machine  had  progressed  by 
means  of  a  very  large  number  of  hardly  discernible 
steps. 

The  object  of  this  and  of  the  preceding  chapter  has 
been  first  to  dwell  on  the  fact  of  inheritance  beinof 
"particulate,"  secondly  to  show  how  this  fact  is  com- 
patible with  the  existence  of  various  types,  some  of 
which  are   subordinate  to  others,  and  thirdly  to  argue 


34  NATURAL  INHERITANCE.  [chap.  hi. 

that  Evolution  need  not  proceed  by  small  steps  only.  I 
have  largely  used  metaphor  and  illustratioD  to  explain 
the  facts,  wishing  to  avoid  entanglements  with  theory 
as  far  as  possible,  inasmuch  as  no  complete  theory  of 
inheritance  has  yet  been  propounded  that  meets  with 
general  acceptation. 


CHAPTEK  TV, 

SCHEMES    OF   DISTEIBUTION  AIN'D    OF   FEEQUENCY. 

Fraternities  and  Populations  to  be  treated  as  Units. — Scliemes  of  Distribu- 
tion and  their  Grades. — The  Shape  of  Schemes  is  independent  of  the 
number  of  observations. — Data  for  Eighteen  Schemes. — Application 
of  the  method  of  Schemes  to  inexact  Measures. — Schemes  of  Fre- 
quency, 

Fraternities  and  Populations  to  he  Treated  as  Units. — 
The  science  of  heredity  is  concerned  with  Fraternities 
and  large  Populations  rather  than  with  individnals,  and 
mnst  treat  them  as  units.  A  compendious  method  is 
therefore  requisite  by  which  we  may  express  the  dis- 
tribution of  each  faculty  among  the  members  of  any 
large  group,  whether  it  be  a  Fraternity  or  an  entire 
Population. 

The  knowledge  of  an  average  value  is  a  meagre  piece 
of  information.  How  little  is  conveyed  by  the  bald 
statement  that  the  average  income  of  English  families  is 
100^.  a  year,  compared  with  what  we  should  learn  if  w^e 
were  told  how  English  incomes  were  distributed  ;  what 
proportion  of  our  countrymen  had  just  and  only  just 
enough  means  to  ward  off  starvation,  and  what  were  the 

D  2 


36  NATURAL   INHERITANCE.  [ohap. 

proportions  of  those  who  had  incomes  in  each  and  every 
other  degree,  up  to  the  huge  annual  receipts  of  a  few 
great  speculators,  manufacturers,  and  landed  proprietors. 
So  in  respect  to  the  distribution  of  any  human  quality 
or  faculty,  a  knowledge  of  mere  averages  tells  but  little  ; 
we  want  to  learn  how  the  quality  is  distributed  among 
the  various  members  of  the  Fraternity  or  of  the  Popula- 
tion, and  to  express  what  we  know  in  so  compact  a 
form  that  it  can  be  easily  grasped  and  dealt  with. 
A  parade  of  great  accuracy  is  foolish,  because  precision 
is  unattainable  in  biological  and  social  statistics  ;  their 
results  being  never  strictly  constant.  Over-minuteness 
is  mischievous,  because  it  overwhelms  the  mind  with 
more  details  than  can  be  compressed  into  a  single 
view.  We  require  no  more  than  a  fairly  just  and 
comprehensive  method  of  expressing  the  way  in  which 
each  measurable  quality  is  distributed  among  the 
members  of  any  group,  whether  the  group  consists 
of  brothers  or  of  members  of  any  particular  social, 
local,  or  other  body  of  persons,  or  whether  it  is  co- 
extensive with  an  entire  nation  or  race. 

A  knowledge  of  the  distribution  of  any  quality  en- 
ables us  to  ascertain  the  Eank  that  each  man  holds 
among  his  fellows,  in  respect  to  that  quality.  This  is 
a  valuable  piece  of  knowledge  in  this  struggling  and 
competitive  world,  where  success  is  to  the  foremost,  and 
failure  to  the  hindmost,  irrespective  of  absolute  efficiency. 
A  blurred  vision  would  be  above  all  price  to  an  in- 
dividual man  in  a  nation  of  blind  men,  though  it  would 
hardly  enable  him  to  earn  his  bread  elsewhere.     When 


IV.]     SCHEMES  OF  DISTRIBUTION  AND  OF  FREQUENCY.     37 

tlie  distribution  of  any  faculty  has  been  ascertained,  we 
can  tell  from  the  measurement,  say  of  our  child,  how  he 
ranks  among  other  children  in  respect  to  that  faculty, 
whether  it  be  a  physical  gift,  or  one  of  health,  or  of 
intellect,  or  of  morals.  As  the  years  go  by,  we  may 
learn  by  the  same  means  whether  he  is  making  his  way 
towards  the  front,  whether  he  just  holds  his  place,  or 
whether  he  is  falling  back  towards  the  rear.  Similarly 
as  regards  the  position  of  our  class,  or  of  our  nation, 
among  other  classes  and  other  nations. 

Schemes  of  Distribution  and  their  Grades. — I  shall 
best  explain  my  graphical  method  of  expressing  Dis- 
tribution, which  I  like  the  more,  the  more  I  use  it, 
and  which  I  have  latterly  much  developed,  by  showing 
how  to  determine  the  Grrade  of  an  individual  among  his 
fellows  in  respect  to  any  particular  faculty.  Suppose 
that  we  have  already  put  on  record  the  measures  of 
many  men  in  respect  to  Strength,  exerted  as  by  an 
archer  in  pulling  his  bow,  and  tested  by  one  of  Salter's 
well-known  dial  instruments  with  a  movable  index. 
Some  men  will  have  been  found  strong  and  others  weak ; 
how  can  we  picture  in  a  compendious  diagram,  or  how 
can  we  define  by  figures,  the  distribution  of  this  faculty 
of  Strength  throughout  the  group  ?  How  shall  we 
determine  and  specify  the  Grade  that  any  particular 
person  would  occupy  in  the  group  ?  The  first  step  is 
to  marshal  our  measures  in  the  orderly  way  familiar  to 
statisticians,  which  is  shown  in  Table  I.  I  usually  work 
to   about  twice  its   degree  of  minuteness,  but  enough 


38 


NATURAL   INHERITANCE. 


[chap. 


has  been  entered  in  the  Table  for  the  purpose  of 
illnstration,  while  its  small  size  makes  it  all  the  more 
intellioible. 

The  fourth  column  of  the  Table  headed  "  Percentages  " 
of  "  Sums  from  the  beginning,"  is  pictorially  translated 
into  Fig.  2,  and  the  third  column  headed  "  Percentages  " 
of  "  No.  of  cases  observed,"  into  Fis^.  3.     The  scale  of 


FIG. 2. 


Us 

100 


80 


-GO 


40 


•''-20 


MiO 


FIG. 3. 


91 


W41 


kjil||l|W|i||in 

|i'i:nj!iIiiimiI 


4D 


— r- 
20 


Ths. 

100 


so 


60 


-40 


'20 


i-0 


lbs.  is  given  at  the  side  of  both  Figs.  :  and  the  com- 
partments a  to  g,  that  are  shaded  with  hrohen  lines, 
have  the  same  meaning  in  both,  but  they  are  differently 
disposed  in  the  two  Figs.  We  will  now  consider  Fig.  2 
only,  which  is  the  one  that  principally  concerns  us. 
The  percentages  in  the  last  column  of  Table  I.  have 
been  marked  off  on  the  bottom  line  of  Fig.  2,  where 
they  are  called  (centesimal)  Grades.  The  number  of 
lbs.  found  in  the  first  column  of  the  Table  determines 


IV.]     SCHEMES  OF  DISTRIBUTION  AND  OF  FREQUENCY.      39 

the  height  of  the  vertical  lines  to  be  erected  at  the 
corresponding  Grades  when  we  are  engaged  in  con- 
structing the  Figure. 

Let  us  bemn  with  the  third  line  in  the  Table  for 
illustration  :  it  tells  us  that  37  per  cent,  of  the  group 
had  Strengths  less  than  70  lbs.  Therefore,  when  drawing 
the  figure,  a  perpendicular  must  be  raised  at  the  37th 
grade  to  a  height  corresponding  to  that  of  70  lbs.  on 
the  side  scale.  The  fourth  line  in  the  Table  tells  us 
that  70  per  cent,  of  the  group  had  Strengths  less  than 
80  lbs.  ;  therefore  a  perpendicular  must  be  raised  at  the 
70th  Grade  to  a  height  corresponding  to  80  lbs.  We 
proceed  in  the  same  way  with  respect  to  the  remaining 
figures,  then  we  join  the  tops  of  these  perpendiculars 
by  straight  lines. 

As  these  observations  of  Strength  have  been  sorted 
into  only  7  groups,  the  trace  formed  by  the  lines  that 
connect  the  tops  of  the  few  perpendiculars  difi'ers  sensibly 
from  a  flowing  curve,  but  when  working  with  double 
minuteness,  as  mentioned  above,  the  connecting  lines 
difi"er  little  to  the  eye  from  the  dotted  curve.  The 
dotted  curve  may  then  be  accepted  as  that  which  would 
result  if  a  separate  perpendicular  had  been  drawn  for 
every  observation,  and  if  permission  had  been  given 
to  slightly  smooth  their  irregularities.  I  call  the  figure 
that  is  bounded  by  such  a  curve  as  this,  a  Scheme  of 
Distribution ;  the  perpendiculars  that  formed  the  scaf- 
folding by  which  it  was  constructed  having  been  first 
rubbed  out.      (See  Fig  4,  next  page.) 

A  Scheme  enables  us  in  a  moment  to  find  the  Grade 


40 


NATURAL    INHERITANCE. 


[chap. 


of  Eank  (on  a  scale  reckoned  from  0°  to  100°)  of  any 
person  in  the  gronp  to  which  he  belongs.  The  measured 
strength  of  the  person  is  to  be  looked  for  in  the  side 
scale  of  the  Scheme  ;  a  horizontal  line  is  thence  drawn 
until  it  meets  the  curve ;  from  the  point  of  meeting 
a  perpendicular  is  dropped  upon  the  scale  of  Grades 
at    the    base  ;    then   the   G-rade    on   which   it   falls   is 


FIG 

.4.          1 

y^ 

- 

/ 

• 

100 


FIG. 5. 


50 


£0° 


100 


IDO" 


100* 


the  one  required.  For  example :  let  us  suppose  the 
Strength  of  Pull  of  a  man  to  have  been  74  lbs., 
and  that  we  wish  to  determine  his  Eank  in  Strength 
among  the  large  group  of  men  who  were  measured 
at  the  Health  Exhibition  in  1884.  We  find  by  Fig. 
4  that  his  centesimal  Grade  is  50°;  in  other  words, 
that  50  per  cent,  of  the  group  will  be  weaker  than 
he    is,     and     50    per    cent,    will     be    stronger.       His 


IV.]     SCHEMES  OF  DISTRIBUTION  AND  OF  FREQUENCY.      41 

position  will  be  exactly  Middlemost,  after  tlie  Strengths 
of  all  the  men  in  the  gronp  have  been  marshalled  in 
the  order  of  their  magnitudes.  In  other  words,  he  is 
of  mediocre  strength.  The  accepted  term  to  express 
the  value  that  occupies  the  Middlemost  position  is 
"  Median,"  which  may  be  used  either  as  an  adjective  or 
as  a  substantive,  but  it  will  be  usually  replaced  in  this 
book  by  the  abbreviated  form  M.  I  also  use  the  word 
"  Mid  "  in  a  few  combinations,  such  as  "  Mid-Fraternity," 
to  express  the  same  thing.  The  Median,  M,  has  three 
properties.  The  first  follows  immediately  from  its  con- 
struction, namely,  that  the  chance  is  an  equal  one,  of 
any  previously  unknown  measure  in  the  group  exceeding 
or  falling  short  of  M.  The  second  is,  that  the  most 
probable  value  of  any  previously  unknown  measure  in 
the  group  is  M.  Thus  if  N  be  any  one  of  the  measures, 
and  u  be  the  value  of  the  unit  in  which  the  measure  is 
recorded,  such  as  an  inch,  tenth  of  an  inch,  &c.,  then 
the  number  of  measures  that  fall  between  (N  -  ^u)  and 
(N  -\r^u),  is  greatest  when  N=:  IVI.  Mediocrity  is  always 
the  commonest  condition,  for  reasons  that  will  become 
apparent  later  on.  The  third  property  is  that  whenever 
the  curve  of  the  Scheme  is  symmetrically  disposed  on 
either  side  of  M,  except  that  one  half  of  it  is  turned 
upwards,  and  the  other  half  downwards,  then  M  is 
identical  with  the  ordinary  Arithmetic  Mean  or  Average. 
This  is  closely  the  condition  of  all  the  curves  I  have  to 
discuss.  The  reader  may  look  on  the  Median  and  on 
the  Mean  as  being  practically  the  same  things,  throughout 
this  book. 


42  NATURAL    INHERITANCE.  [chap. 

It  must  be  understood  that  M,  like  the  Mean  or  the 
Average,  is  almost  always  an  interpolated  value,  corre- 
sponding to  no  real  measure.  If  the  observations  were 
infinitely  numerous  its  position  would  not  differ  more 
than  infinitesimally  from  that  of  some  one  of  them ; 
even  in  a  series  of  one  or  two  hundred  in  number,  the 
difference  is  insignificant. 

Now  let  us  make  our  Scheme  answer  another  question. 
Suppose  we  want  to  know  the  percentage  of  men  in  the 
group  of  which  we  have  been  speaking,  whose  Strength 
lies  between  any  two  specified  limits,  as  between  74  lbs. 
and  64  lbs.  We  draw  horizontal  lines  (Fig.  4)  from 
points  on  the  side  scale  corresponding  to  either  limit, 
and  drop  perpendiculars  upon  the  base,  from  the  points 
where  those  lines  meet  the  curve.  Then  the  number  of 
Grades  in  the  intercept  is  the  answer.  The  Fig.  shows 
that  the  number  in  the  present  case  is  30  ;  therefore 
30  per  cent,  of  the  group. have  Strengths  of  Pull  ranging 
between  74  and  64  lbs. 

We  learn  how  to  transmute  female  measures  of  any 
characteristic  into  male  ones,  by  comparing  their  respec- 
tive schemes,  and  devising  a  formula  that  will  change 
the  one  into  the  other.  In  the  case  of  Stature,  the 
simple  multiple  of  1*08  was  found  to  do  this  with 
sufficient  precision. 

If  we  wish  to  compare  the  average  Strengths  of  two 
different  groups  of  persons,  say  one  consisting  of  men 
and  the  other  of  women,  we  have  simply  to  comjDare 
the  values  at  the  50th  Grades  in  the  two  schemes.  For 
even  if  the  Medians  difi'cr  considerably  from  the  Means, 


IV.]     SCHEMES  OF  DISTRIBUTION  AND  OF  FREQUENCY.      43 

both  the  ratios  and  the  differences  between  either  pair  of 
values  would  be  sensibly  the  same. 

A  different  way  of  comparing  two  Schemes  is  some- 
times useful.  It  is  to  draw  them  in  opposed  directions, 
as  in  Fig.  5,  p.  40.  Their  curves  will  then  cut  each 
other  at  some  point,  whose  Grade  when  referred  to 
either  of  the  two  Schemes  (whichever  of  them  may  be 
preferred),  determines  the  point  at  which  the  same 
values  are  to  be  found.  In  Fig.  5,  the  Grade  in  the 
one  Scheme  is  20° ;  therefore  in  the  other  Scheme  it  is 
100°- 20°,  or  80°.  In  respect  to  the  Strength  of  Pull 
of  men  and  women,  it  appears  that  the  woman  who 
occupies  the  Grade  of  96°  in  her  Scheme,  has  the  same 
strength  as  the  man  who  occupies  the  Grade  of  4°  in  his 
Scheme. 

I  should  add  that  this  great  inequality  in  Strength 
between  the  sexes,  is  confirmed  by  other  measure- 
ments made  at  the  same  time  in  respect  to  the 
Strength  of  their  Squeeze,  as  tested  by  another  of 
Salter's  instruments.  Then  the  woman  in  the  93rd  and 
the  man  in  the  7th  Grade  of  their  resective  Schemes, 
proved  to  be  of  equal  strength.  In  my  paper  ^  on  the 
results  obtained  at  the  laboratory,  I  remarked :  "  Yery 
powerful  women  exist,  but  happily  perhaps  for  the 
repose  of  the  other  sex  such  gifted  women  are  rare. 
Out  of  1,657  adult  women  of  all  ages  measured  at  the 
laboratory,  the  strongest  could  only  exert  a  squeeze  of 
86  lbs.,  or  about  that  of  a  medium  man." 

1  Journ.  Anthropol.  Inst.  1885.  Mem.  :  There  is  a  blunder  in  the  para- 
graph, p.  23,  headed  "Height  Sitting  and  Standing."  The  paragraph 
should  be  struck  out. 


44  NATURAL  INHERITANCE.  [chap. 

The  Shape  of  Schemes  is  Independent  of  the  Number 
of  Observations. — When  Schemes  are  drawn  from  dif- 
ferent samples  of  the  same  large  group  of  measurements, 
though  the  number  in  the  several  samples  may  differ 
greatly,  we  can  always  so  adjust  the  horizontal  scales 
that  the  breadth  of  the  several  Schemes  shall  be  uniform. 
Then  the  shaj)es  of  the  Schemes  drawn  from  different 
samples  will  be  little  affected  by  the  number  of  observa- 
tions used  in  each,  supposing  of  course  that  the  numbers 
are  never  too  small  for  ordinary  statistical  purposes. 
The  only  recognisable  differences  between  the  Schemes 
will  be,  that,  if  the  number  of  observations  in  the 
sample  is  very  large,  the  upper  margin  of  the  Scheme 
will  fall  into  a  more  regular  curve,  especially  towards 
either  of  its  limits.  Some  irregularity  will  be  found  in 
the  above  curve  of  the  Strength  of  Pull ;  but  if  the 
observations  had  been  ten  times  more  numerous,  it  is 
probable,  judging  from  much  experience  of  such  curves, 
that  the  irregularity  would  have  been  less  consjoicuous, 
and  perhaps  would  have  disappeared  altogether. 

However  numerous  the  observations  may  be,  the 
curve  will  always  be  uncertain  and  incomplete  at  its 
extreme  ends,  because  the  next  value  may  happen  to  be 
greater  or  less  than  any  one  of  those  that  preceded  it. 
Again,  the  position  of  the  first  and  the  last  observation, 
supposing  each  observation  to  have  been  laid  down  sepa- 
rately, can  never  coincide  with  the  adjacent  limit.  The 
more  numerous  the  observations,  and  therefore  the  closer 
the  perpendiculars  by  which  they  are  represented,  the 
nearer  will  the  two  extreme  perpendiculars  approach  the 


IV]     SCHEiMES  OF  DISTRIBUTION  AND  OF  FREQUENCY.     45 

limits,  but  they  will  never  actually  touch  them.    A  chess 
board  has  eight  squares  in  a  row,  and  eight  pieces  may  be 
arranged  in  order  on  any  one  row,  each  piece  occupying 
the  centre  of  a  square.     Let  the  divisions  in  the  row  be 
graduated,   calling  the  boundary  to   the   extreme  left, 
0°.     Then  the  successive  divisions  between  the  squares 
will  be    1°,  2°,  3°,  up  to  7°,  and  the  boundary  to  the 
extreme  right  will  be  8°.     It  is  clear  that  the  position  of 
the  first  piece  lies  half-way  between  the  grades  (in  a 
scale  of  eight  grades)  of  0°  and  1° ;  therefore  the  grade 
occupied  by  the  first  piece  would  be   counted  on  that 
scale  as  0*5°;  also  the   grade  of  the  last  piece  as  7 '5°. 
Or  again,  if  we  had  800   pieces,  and  the  same  number 
of  class-places,  the   grade  of  the  first  piece,  in  a  scale 
of  800  grades,  would  exceed  the  grade  0°,  by  an  amount 
equal  to    the  width    of   one   half-place    on   that  scale, 
while  the  last  of  them  would  fall  short  of  the  800th 
grade  by  an  equal  amount.     This  half-place  has  to  be 
attended  to   and  allowed   for  when  schemes    are    con- 
structed   from    comparatively    few    observations,    and 
always  when  values  that  are  very  near  to  either  of  the 
centesimal   grades    0°    or   100°  are  under   observation ; 
but  between  the   centesimal  grades  of  5°  and  95°  the 
influence  of  a  half  class-place  upon  the  value  of  the 
corresponding  observation  is  insignificant,  and  may  be 
disregarded.      It  will  not  henceforth   be    necessary  to 
repeat  the  word  centesimal.     It  will  be  always  implied 
when   nothing   is    said   to    the    contrary,   and    nothing 
henceforth  will  be  said  to  the  contrary.     The  word  will 
be  used  for  the  last  time  in  the  next  paragraph. 


46  NATURAL  INHERITANCE.  [chap. 

Data  for  Eighteen  Schemes. — Sufficient  data  for  re- 
constructing any  Scheme,  witli  niucli  correctness,  may 
be  printed  in  a  single  line  of  a  Table,  and  according  to 
a  uniform  plan  tbat  is  suitable  for  any  kind  of  values. 
The  measures  to  be  recorded  are  those  at  a  few  definite 
G-rades,  beginning  say  at  5°,  ending  at  95°,  and  including 
every  intermediate  tenth  Grade  from  10°  to  90°.  It  is 
convenient  to  add  those  at  the  Grades  25°  and  75°,  if 
space  permits.  The  former  values  are  given  for  eighteen 
different  Schemes,  in  Table  2.  In  the  memoir  from 
which  that  table  is  reprinted,  the  values  at  what  I  now 
call  (centesimal)  Grades,  were  termed  Percentiles.  Thus 
the  values  at  the  Grades  5°  and  10°  would  be  respectively 
the  5th  and  the  10th  percentile.  It  still  seems  to  me 
that  the  word  percentile  is  a  useful  and  expressive 
abbreviation,  but  it  will  not  be  necessary  to  employ  it 
in  the  present  book.  It  is  of  course  unadvisable  to  use 
more  technical  words  than  is  absolutely  necessary,  and 
it  will  be  possible  to  get  on  without  it,  by  the  help  of 
the  new  and  more  important  word  "  Grade." 

A  series  of  Schemes  that  express  the  distribution  of 
various  faculties,  is  valuable  in  an  anthropometric  labora- 
tory, for  they  enable  every  person  who  is  measured  to 
find  his  Rank  or  Grade  in  each  of  them. 

Diagrams  may  also  be  constructed  by  drawing  parallel 
lines,  each  divided  into  100  Grades,  and  entering  each 
round  number  of  inches,  lbs.,  &c.,  at  their  proper  places. 
A  diagram  of  this  kind  is  very  convenient  for  reference, 
but  it  does  not  admit  of  being  printed ;  it  must  be 
drawn  or  lithographed.     I  have  constructed  one  of  these 


IV.]     SCHEMES  OF  DISTRIBUTION  AND  OF  FREQUENCY.     47 

from  tlie  18  Schemes,  and  find  it  is  easily  understood 
and  mucli  used  at  my  laboratory. 

Application  of  Schemes  to  Inexact  Measures. — Schemes 
of  Distribution  may  be  constructed  from  observations 
that  are  barely  exact  enough  to  deserve  to  be  called 
measures. 

I  will  illustrate  the  method  of  doing  so  by  marshalling 
the  data  contained  in  a  singularly  interesting  little 
memoir  written  by  Sir  James  Paget,  into  the  form  of 
such  a  Scheme.  The  memoir  is  published  in  vol.  v.  of  St. 
Bartholomew's  Hospital  Eeports,  and  is  entitled  "  What 
Becomes  of  Medical  Students."  He  traced  with  great 
painstaking  the  career  of  no  less  than  1,000  pupils  who 
had  attended  his  classes  at  that  Hospital  during  various 
periods  and  up  to  a  date  15  years  previous  to  that  at 
which  his  memoir  was  written.  He  thus  did  for  St. 
Bartholomew's  Hospital  what  has  never  yet  been  done, 
so  far  as  I  am  aware,  for  any  University  or  Public 
School,  whose  historians  count  the  successes  and  are 
silent  as  to  the  failures,  giving  to  inquirers  no  adequate 
data  for  ascertaining  the  real  value  of  those  institutions 
in  English  Education.  Sir  J.  Paget  divides  the  successes 
of  his  pupils  in  their  profession  into  fiYQ  grades,  all  of 
which  he  carefully  defines ;  they  are  distinguished ; 
considerable ;  moderate ;  very  limited  success ;  and 
failures.  Several  of  the  students  had  left  the  profes- 
sion either  before  or  after  taking  their  degrees,  usually 
owing  to  their  unfitness  to  succeed,  so  after  analysing 
the  accounts  of  them  given  in  the  memoir,  I  drafted 


48  NATURAL  INHERITANCE.  [chap. 

several  into  the  list  of  failures  and  distributed  the  rest, 
with  the  result  that  the  number  of  cases  in  the  successive 
classes,  amounting  now  to  the  full  total  of  1,000,  became 
28,  80,  616,  151,  and  125.  This  differs,  I  should  say, 
a  Kttle  from  the  inferences  of  the  author,  but  the  matter 
is  here  of  small  importance,  so  I  need  not  go  further  into 
details. 

If  a  Scheme  is  drawn  from  these  figures,  in  the  way 
described  in  page  39,  it  will  be  found  to  have  the 
characteristic  shape  of  our  familiar  curve  of  Distribution. 
If  we  wished  to  convey  the  utmost  information  that  this 
Scheme  is  capable  of  giving,  we  might  record  in  much 
detail  the  career  of  two  or  three  of  the  men  who  are 
clustered  about  each  of  a  few  selected  Grades,  such  as 
those  that  are  used  in  Table  11. ,  or  fewer  of  them.  I 
adopted  this  method  when  estimating  the  variability  of 
the  Visualising  Power  (Inquiries  into  Human  Faculty). 
My  data  were  very  lax,  but  this  method  of  treatment 
got  all  the  good  out  of  them  that  they  possessed.  In 
the  present  case,  it  appears  that  towards  the  foremost 
of  the  successful  men  within  fifteen  years  of  taking 
their  degrees,  stood  the  three  Professors  of  Anatomy 
at  Oxford,  Cambridge,  and  Edinburgh ;  that  towards 
the  bottom  of  the  failures,  lay  two  men  who  committed 
suicide  under  circumstances  of  great  disgrace,  and  lowest 
of  all  Palmer,  the  Rugeley  murderer,  who  was  hanged. 

We  are  able  to  compare  any  two  such  Schemes  as  the 
above,  with  numerical  precision.  The  want  of  exactness 
in  the  data  from  which  they  are  drawn,  will  of  course 
cling  to  the  result,  but  no  new  error  will  l^e  introduced 


IV.]     SCHEMES  OF  DISTRIBUTION  AND  OF  FREQUENCY.     49 

by  the  process  of  comparison.  Suppose  the  second 
Scheme  to  refer  to  the  successes  of  students  from  another 
hospital,  we  should  draw  the  two  Schemes  in  opposed 
directions,  just  as  was  done  in  the  Strength  of  Pull  of 
Males  and  Females,  Fig.  5,  and  determine  the  Grrade 
in  either  of  the  Schemes  at  which  success  was  equal. 

Schemes  of  Frequency. — The  method  of  arranging 
observations  in  an  orderly  manner  that  is  generally 
employed  by  statisticians,  is  shown  in  Fig.  3,  page  38, 
which  expresses  the  same  facts  as  Fig.  2  under  a  different 
aspect,  and  so  gives  rise  to  the  well-known  Curve  of 
"Frequency  of  Error,"  though  in  Fig.  3  the  curve  is 
turned  at  right  angles  to  the  position  in  which  it  is 
usually  drawn.  It  is  so  placed  in  order  to  show  more 
clearly  its  relation  to  the  Curve  of  Distribution.  The 
Curve  of  Frequency  is  far  less  convenient  than  that  of 
Distribution,  for  the  purposes  just  described  and  for 
most  of  those  to  be  hereafter  spoken  of.  But  the  Curve 
of  Frequency  has  other  uses,  of  which  advantage  will 
be  taken  later  on,  and  to  which  it  is  unnecessary  now 
to  refer. 

A  Scheme  as  explained  thus  far,  is  nothing  more  than 
a  compendium  of  a  mass  of  observations  which,  on  being 
marshalled  in  an  orderly  manner,  fall  into  a  diagram 
whose  contour  is  so  regular,  simple,  and  bold,  as  to 
admit  of  being  described  by  a  few  numerals  (Table  2), 
from  which  it  can  at  any  time  be  drawn  afresh.  The 
regular  distribution  of  the  several  faculties  among  a 
large  population  is  little  disturbed  by  the  fact  that  its 

E 


50  NATURAL  INHERITANCE.  [chap.  iv. 

members  are  varieties  of  different  types  and  sub-types. 
So  the  distribution  of  a  heavy  mass  of  foliage  gives  little 
indication  of  its  growth  from  separate  twigs,  of  separate 
branches,  of  separate  trees. 

The  application  of  theory  to  Schemes,  their  approxi- 
mate description  by  only  two  values,  and  the  properties 
of  their  bounding  Curves,  will  be  described  in  the  next 
chapter. 


CHAPTER   y. 

NOEMAL   VAEIABILITY. 

Schemes  of  Deviations. — Normal  Curve  of  Distribution. — Comparison  of 
the  observed  with  the  Normal  Curve. — Tlie  value  of  a  single  Devia- 
tion at  a  known  Grade  determines  a  Normal  Scheme  of  Deviations. — 
Two  Measures  at  two  known  Grades  determine  a  Normal  Scheme 
of  Measures. — The  Charms  of  Statistics. — Mechanical  illustration  of 
the  Cause  of  the  Curve  of  Frequency. — Order  in  apparent  Chaos. — 
Problems  in  the  Law  of  Error. 

Schemes  of  Deviations. — We  have  now  seen  how  easy 
it  is  to  represent  the  distribution  of  any  qnality  among  a 
multitude  of  men,  either  by  a  simple  diagram  or  by  a  line 
containing  a  few  figures.  In  this  chapter  it  will  be  shown 
that  a  considerably  briefer  description  is  approximately 
sufficient. 

Every  measure  in  a  Scheme  is  equal  to  its  Middlemost, 
or  Median  value,  or  ^,plus  or  minus  a  certain  Devia- 
tion from  M.  The  Deviation,  or  "Error"  as  it  is 
technically  called,  is  plus  for  all  grades  above  50°,  zero 
for  50°,  and  minus  for  all  grades  below  50°.  Thus  if 
(±D)  be  the  deviation  from  IVI  in  any  particular  case, 
every  measure  in  a  Scheme  may  be  expressed  in  the 

E  2 


52  NATURAL  INHERITANCE.  [chap. 

form  of  IV1  +  (±D).  If  IVI  =  0,  or  if  it  is  subtracted 
from  every  measure,  the  residues  wliicli  are  tlie  different 
values  of  ( ±  D)  will  form  a  Scheme  by  themselves. 
Schemes  may  therefore  be  made  of  Deviations  as  well  as 
of  Measures,  and  one  of  the  former  is  seen  in  the 
upper  part  of  Fig.  6,  page  40.  It  is  merely  the  upper 
portion  of  the  corresponding  Scheme  of  Measures,  in 
which  the  axis  of  the  curve  plays  the  part  of  the  base. 

A  strong  family  likeness  runs  between  the  1 8  different 
Schemes  of  Deviations  that  may  be  respectively  derived 
from  the  data  in  the  18  lines  of  Table  2.  If  the  slope 
of  the  curve  in  one  Scheme  is  steeper  than  that  of 
another,  we  need  only  to  fore-shorten  the  steeper 
Scheme,  by  inclining  it  away  from  the  line  of  sight,  in 
order  to  reduce  its  apparent  steepness  and  to  make  it 
look  almost  identical  with  the  other.  Or,  better  still, 
we  may  select  appropriate  vertical  scales  that  will  enable 
all  the  Schemes  to  be  drawn  afresh  with  a  uniform  slope, 
and  be  made  strictly  comparable. 

Suppose  that  we  have  only  two  Schemes,  A.  and  b., 
that  we  wish  to  compare.  Let  L.i,  L.2  be  the  lengths  of 
the  perpendiculars  at  two  specified  grades  in  Scheme  A., 
and  K.i  K.2  the  lengths  of  those  at  the  same  grades  in 
Scheme  b.  ;  then  if  every  one  of  the  data  from  which 

Scheme   b.    was    drawn   be   multiplied   by   ^^      ^'^' ,  a 

series  of  transmuted  data  will  be  obtained  for  drawing 
a  new  Scheme  b'.,  on  such  a  vertical  scale  that  its 
general  slope  between  the  selected  grades  shall  be  the 
same  as  in  Scheme  A.     For  practical  convenience  the 


v.]  NORMAL  VARIABILITY.  53 

selected  Grades  will  be  always  those  of  25°  and  75°. 
They  stand  at  the  first  and  third  quarterly  divisions  of 
the  base,  and  are  therefore  easily  found  by  a  pair  of 
compasses.  They  are  also  well  placed  to  afford  a  fair 
criterion  of  the  general  slope  of  the  Curve.  If  we  call 
the  perpendicular  at  25°,  Q.i ;  and  that  at  75°,  Q.2, 
then  the  unit  by  which  every  Scheme  will  be  defined 
is  its  value  of  -^(0.2- Q-i),  and  will  be  called  its 
Q.  As  the  M  measures  the  Average  Height  of  the 
curved  boundary  of  a  Scheme,  so  the  Q  measures  its 
general  slope.  When  we  wish  to  transform  many  difi'er- 
ent  Schemes,  numbered  I.,  II.,  III.,  &c.,  whose  respective 
values  of  Q  are  qi,  q^,  q^,  Sec,  to  others  whose  values  of  Q 
are  in  each  case  equal  to  qo,  then  all  the  data  from  which 

Scheme  I.  was  drawn,  must  be  multiplied  by  ^ ;  those 

from  which  Scheme  II.  was  drawn,  by  ^,  and  so  on,  and 

new  Schemes  have  to  be  constructed  from  these  trans- 
muted values. 

Our  Q  has  the  further  merit  of  being  practically  the 
same  as  the  value  which  mathematicians  call  the 
"  Probable  Error,"  of  which  we  shall  speak  further  on. 

Want  of  space  in  Table  2  prevented  the  insertion  of 
the  measures  at  the  Grades  25°  and  75°,  but  those  at 
20°  and  30°  are  given  on  the  one  hand,  and  those  at  70** 
and  80°  on  the  other,  whose  respective  averages  diff'er 
but  little  from  the  values  at  25°  and  75°.  I  therefore 
will  use  those  four  measures  to  obtain  a  value  for  our 
unit,  which  we  will  call  Q^,  to  distinguish  it  from  Q. 


54  NATURAL  INHERITANCE.  [chap. 

These  are  not  identical  in  value,  because  the  outline  of 
the  Scheme  is  a  curved  and  not  a  straight  line,  but  the 
difference  between  them  is  small,  and  is  approximately 
the  same  in  all  Schemes.  It  will  shortly  be  seen  that 
Q'=  1*015  xQ  approximately;  therefore  a  series  of  De- 
viations measured  in  terms  of  the  large  unit  Q'  are 
numerically  smaller  than  if  they  had  been  measured  in 
terms  of  the  small  unit  (for  the  same  reason  that  the 
numerals  in  2,  3,  kQ.^feet  are  smaller  than  those  in  the 
corresponding  values  of  24,  36,  &c.,  inches),  and  they 
must  be  multiplied  by  1.015  when  it  is  desired  to 
change  them  into  a  series  having  the  smaller  value  of  Q 
for  their  unit. 

All  the  18  Schemes  of  Deviation  that  can  be  derived 
from  Table  2  have  been  treated  on  these  principles,  and 
the  results  are  given  in  Table  3.  Their  general  accord- 
ance with  one  another,  and  still  more  with  the  mean  of 
all  of  them,  is  obvious. 

Normal  Curve  of  Distribution. — The  values  in  the 
bottom  line  of  Table  3,  which  is  headed  "  Normal  Values 
when  Q  =  1,"  and  which  correspond  with  minute  pre- 
cision to  those  in  the  line  immediately  above  them,  are 
not  derived  from  observations  at  all,  but  from  the  well- 
known  Tables  of  the  "  Probability  Integral "  in  a  way 
that  mathematicians  will  easily  understand  by  comparing 
the  Tables  4  to  8  inclusive.  I  need  hardly  remind  the 
reader  that  the  Law  of  Error  upon  which  these  Normal 
Values  are  based,  was  excogitated  for  the  use  of  astro- 
nomers  and   others  who   are   concerned  with   extreme 


v.]  NORMAL  VARIABILITY.  55 

accuracy  of  measurement,  and  without  tlie  slightest  idea 
until  the  time  of  Quetelet  that  they  might  be  applicable 
to  human  measures.  But  Errors,  Differences,  Deviations, 
Divergencies,  Dispersions,  and  individual  Variations,  all 
spring  from  the  same  kind  of  causes.  Objects  that  bear 
the  same  name,  or  can  be  described  by  the  same  phrase, 
are  thereby  acknowledged  to  have  common  points  of 
resemblance,  and  to  rank  as  members  of  the  same  species, 
class,  or  whatever  else  we  may  please  to  call  the  group. 
On  the  other  hand,  every  object  has  Differences  peculiar 
to  itself,  by  which  it  is  distinguished  from  others. 

This  general  statement  is  applicable  to  thousands  of 
instances.  The  Law  of  Error  finds  a  footing  wherever 
the  individual  peculiarities  are  wholly  due  to  the  com- 
bined influence  of  a  multitude  of  "  accidents,"  in  the 
sense  in  which  that  word  has  already  been  defined. 
All  persons  conversant  with  statistics  are  aware  that 
this  supposition  brings  Variability  within  the  grasp 
of  the  laws  of  Chance,  with  the  result  that  the 
relative  frequency  of  Deviations  of  different  amounts 
admits  of  being  calculated,  when  those  amounts  are 
measured  in  terms  of  any  self-contained  unit  of  varia- 
bility, such  as  our  Q.  The  Tables  4  to  8  give  the 
results  of  these  purely  mathematical  calculations,  and 
the  Curves  based  upon  them  may  with  propriety  be 
distinguished  as  ''  Normal."  Tables  7  and  8  are  based 
upon  the  familiar  Table  of  the  Probability  Integral, 
given  in  Table  5,  via  that  in  Table  6,  in  which  the  unit 
of  variability  is  taken  to  be  the  "  Probable  Error  "  or 
our  Q,  and  not  the  "Modulus."     Then  I  turn  Table  6 


56  NATURAL  INHERITANCE.  [chap. 

inside  out,  as  it  were,  deriving  the  "  arguments "  for 
Tables  7  and  8  from  tlie  entries  in  the  body  of  Table  6, 
and  making  other  easily  intelligible  alterations. 

Comparison  of  the  Observed  ivith  the  Normal  Curve. 
— I  confess  to  having  been  amazed  at  the  extraordinary 
coincidence  between  the  two  bottom  lines  of  Table  3, 
considering  the  great  variety  of  faculties  contained  in 
the  1 8  Schemes  ;  namely,  three  kinds  of  linear  measure- 
ment, besides  one  of  weight,  one  of  capacity,  two  of 
strength,  one  of  vision,  and  one  of  swiftness.  It  is 
obvious  that  weight  cannot  really  vary  at  the  same  rate 
as  height,  even  allowing  for  the  fact  that  tall  men  are 
often  lanky,  but  the  theoretical  impossibility  is  of  the 
less  practical  importance,  as  the  variations  in  weight  are 
small  compared  to  the  weight  itself.  Thus  we  see  from 
the  value  of  Q  in  the  first  column  of  Table  3,  that  half 
of  the  persons  deviated  from  their  M  by  no  more  than 
10  or  11  lbs.,  which  is  about  one-twelfth  part  of  the 
value  of  IVI.  Although  the  several  series  in  Table  3  run 
fairly  well  together,  I  should  not  have  dared  to  hope 
that  their  irregularities  would  have  balanced  one  another 
so  beautifully  as  they  have  done.  It  has  been  objected 
to  some  of  my  former  work,  especially  in  Hereditary 
Genius,  that  I  pushed  the  applications  of  the  Law  of 
Frequency  of  Error  somewhat  too  far.  I  may  have  done 
so,  rather  by  incautious  phrases  than  in  reality ;  but 
I  am  sure  that,  with  the  evidence  now  before  us,  the 
applicability  of  that  law  is  more  than  justified  within 
the  reasonable  limits  asked  for  in  the  present  book.     I 


v.]  NORMAL  VARIABILITY.  57 

am  satisfied  to  claim  that  the  Normal  Curve  is  a  fair 
average  representation  of  the  Observed  Curves  during 
nine-tenths  of  their  course ;  that  is,  for  so  much  of 
them  as  lies  between  the  grades  of  5°  and  95°.  In 
particular,  the  agreement  of  the  Curve  of  Stature  with 
the  Normal  Curve  is  very  fair,  and  forms  a  mainstay  of 
my  inquiry  into  the  laws  of  Natural  Inheritance. 

It  has  already  been  said  that  mathematicians  laboured 
at  the  law  of  Error  for  one  set  of  purposes,  and  we 
are  entering  into  the  fruits  of  their  labours  for  another. 
Hence  there  is  no  ground  for  surprise  that  their  Nomen- 
clature is  often  cumbrous  and  out  of  place,  when  applied 
to  problems  in  heredity.  This  is  especially  the  case 
with  regard  to  their  term  of  "  Probable  Error,"  by  which 
they  mean  the  value  that  one  half  of  the  Errors  exceed 
and  the  other  half  fall  short  of  This  is  practically  the 
same  as  our  Q.-^  It  is  strictly  the  same  whenever  the 
two  halves  of  the  Scheme  of  Deviations  to  which  it 
applies  are  symmetrically  disposed  about  their  common 
axis. 

The  term  Probable  Error,  in  its  plain  English  inter- 
pretation of  the  most  Probable  Error,  is  quite  mis- 
leading, for  it  is  not  that.  The  most  Probable  Error 
(as  Dr.  Venn  has  pointed  out,  in  his  Logic  of  Chance) 

1  The  following  little  Table  may  be  of  service  : — 

Values  of  the  different  Constants  when  the  Proh.  Error  is  tahen  as  unity,  and 

their  corresponding   Grades. 


Prob.  Error I'OOO 

Modulus 2-097 

Mean  Error 1-183 

Error  of  Mean  Squares  1-483 


corresponding  Grades  25°-0,  75° -0 

r-9,  92°-l 
„  „        21°-2,  78°-8 


16°-0,  84°-0 


58  NATURAL  INHERITANCE.  [chap. 

is  zero.  This  results  from  what  was  said  a  few  pages 
back  about  the  most  probable  measure  in  a  Scheme 
being  its  IVI.  In  a  Scheme  of  Errors  the  M  is  equal  to 
0,  therefore  the  most  Probable  Error  in  such  a  Scheme 
is  0  also.  It  is  astonishing  that  mathematicians,  who 
are  the  most  precise  and  perspicacious  of  men,  have  not 
long  since  revolted  against  this  cumbrous,  slip-shod, 
and  misleading  phrase.  They  really  mean  what  I 
should  call  the  Mid-Error,  but  their  phrase  is  too  firmly 
established  for  me  to  uproot  it.  I  shall  however  always 
write  the  word  Probable  when  used  in  this  sense,  in  the 
form  of  "  Prob.  " ;  thus  "  Prob.  Error,"  as  a  continual 
protest  against  its  illegitimate  use,  and  as  some  slight 
safeguard  against  its  misinterpretation.  Moreover  the 
term  Probable  Error  is  absurd  when  applied  to  the 
subjects  now  in  hand,  such  as  Stature,  Eye-colour, 
Artistic  Faculty,  or  Disease.  I  shall  therefore  usually 
speak  of  Prob.  Deviation. 

Though  the  value  of  our  Q  is  the  same  as  that  of 
the  Prob.  Deviation,  Q  is  not  a  convertible  term  with 
Prob.  Deviation.  We  shall  often  have  to  speak  of  the 
one  without  immediate  reference  to  the  other,  just  as 
we  speak  of  the  diameter  of  the  circle  without  reference 
to  any  of  its  properties,  such  as,  if  lines  are  drawn  from 
its  ends  to  any  point  in  the  circumference,  they  will 
meet  at  a  right  angle.  The  Q  of  a  Scheme  is  as  de- 
finite a  phrase  as  the  Diameter  of  a  Circle,  but  we 
cannot  replace  Q  in  that  phrase  by  the  words  Prob. 
Deviation,  and  speak  of  the  Prob.  Deviation  of  a 
Scheme,  without  doing  some  violence  to  lanoaiao^e.     We 


v.]  NORMAL  VARIABILITY.  59 

should  have  to  express  ourselves  from  another  point  of 
view,  and  at  much  greater  length,  and  say  "the  Prob. 
Deviation  of  any,  as  yet  unknown  measure  in  the  Scheme, 
from  the  Mean  of  all  the  measures  from  which  the 
Scheme  was  constructed." 

The  primary  idea  of  Q  has  no  reference  to  the  existence 
of  a  Mean  value  from  which  Deviations  take  place.  It 
is  half  the  difference  between  the  measures  found  at  the 
25th  and  75th  Centesimal  Grades.  In  this  definition 
there  is  not  the  slightest  allusion,  direct  or  indirect,  to 
the  measure  at  the  50th  Grade,  which  is  the  value  of  M. 
It  is  perfectly  true  that  the  measure  at  Grade  25°  is 
IVI — Q,  and  that  at  Grade  75°  is  IVI  +  Q,  but  all  this  is 
superimposed  upon  the  primary  conception.  Q  stands 
essentially  on  its  own  basis,  and  has  nothing  to  do  with 
IVI.  It  will  often  happen  that  we  shall  have  to  deal 
with  Prob  :  Deviations,  but  that  is  no  reason  why  we 
should  not  use  Q  whenever  it  suits  our  purposes  better, 
especially  as  statistical  statements  tend  to  be  so  cum- 
brous that  every  abbreviation  is  welcome. 

The  stage  to  which  we  have  now  arrived  is  this.  It 
has  been  shown  that  the  distribution  of  very  different 
human  qualities  and  faculties  is  approximately  Normal, 
and  it  is  inferred  that  with  reasonable  precautions  we 
may  treat  them  as  if  they  were  wholly  so,  in  order  to 
obtain  approximate  results.  We  shall  thus  deal  with  an 
entire  Scheme  of  Deviations  in  terms  of  its  Q,  and  with 
an  entire  Scheme  of  Measures  in  terms  of  its  IVI  and  Q, 
just  as  we  deal  with  an  entire  Circle  in  terms   of  its 


60  NATURAL  INHERITANCE.  [chap. 

radius,  or  with  an  entire  Ellipse  in  terms  of  its  major 
and  minor  axes.  We  can  also  apply  tlie  various  beau- 
tiful properties  of  the  Law  of  Frequency  of  Error  to 
the  observed  values  of  Q.  In  doing  so,  we  act  like 
woodsmen  who  roughly  calculate  the  cubic  contents  of 
the  trunk  of  a  tree,  by  measuring  its  length,  and  its  girth 
at  either  end,  and  submitting  their  measures  to  formulae 
that  have  been  deduced  from  the  properties  of  ideally 
perfect  straight  lines  and  circles.  Their  results  prove 
serviceable,  although  the  trunk  is  only  rudely  straight 
and  circular.  I  trust  that  my  results  will  be  yet  closer 
approximations  to  the  truth  than  those  usually  arrived 
at  by  the  woodsmen. 

The  value  of  a  single  Deviation  at  a  known  Grade 
determines  a  Normal  Scheme  of  Deviations, — When 
Normal  Curves  of  Distribution  are  drawn  within  the 
same  limits,  they  differ  from  each  other  only  in  their 
general  slope ;  and  the  slope  is  determined  if  the  value 
of  the  Deviation  is  given  at  any  one  specified  G-rade. 
It  must  be  borne  in  mind  that  the  width  of  the  limits 
between  which  the  Scheme  is  drawn,  has  no  influence  on 
the  values  of  the  Deviations  at  the  various  Grades, 
because  the  latter  are  proportionate  parts  of  the  base. 
As  the  limits  vary  in  width,  so  do  the  intervals  between 
the  Grades.  When  measuring  the  Deviation  at  a  speci- 
fied Grade  for  the  purpose  of  determining  the  whole 
Curve,  it  is  of  course  convenient  to  adhere  to  the  same 
Grade  in  all  cases.  It  will  be  recollected  that  when 
dealing  with  the  observed  curves  a  few  pages  back,  I 


v.]  NORMAL  VARIABILITY.  61 

used  not  one  Grade  but  two  Grades  for  the  purpose, 
namely  25°  and  75°  ;  but  in  tbe  Normal  Curve,  the 
plus  and  minus  Deviations  are  equal  in  amount  at  all 
pairs  of  symmetrical  distances  on  either  side  of  grade 
50° ;  therefore  the  Deviation  at  either  of  the  Grades  25° 
or  75°  is  equal  to  Q,  and  suffices  to  define  the  entire 
Curve. 

The  reason  why  a  certain  value  Q'  was  stated  a  few 
pages  back  to  be  equal  to  1'015  Q,  is  that  the  Normal 
Deviations  at  20°  and  at  30°,  (whose  average  we  called 
Q')  are  found  in  Table  8,  to  be  1*25  and  078;  and 
similarly  those  at  70°  and  60°.  The  average  of  1*25 
and  0"78  is  1'015,  whereas  the  Deviation  at  25°  or  at 
75°  is   1-000. 

Tivo  Measures  at  known  Grades  determine  a  Normal 
Scheme  of  Measures. — If  we  know  the  value  of  IVI  as 
well  as  that  of  Q  we  know  the  entire  Scheme.  IVI  ex- 
presses the  mean  value  of  all  the  objects  contained  in 
the  group,  and  Q  defines  their  variability.  But  if  we 
know  the  Measures  at  any  two  specified  Grades,  we  can 
deduce  IVI  and  Q  from  them,  and  so  determine  the  entire 
Scheme.  The  method  of  doing  this  is  explained  in  the 
foot-note.^ 

1  The  following  is  a  fuller  description  of  the  propositions  in  this  and 
in  the  preceding  paragraph  : — 

(1)  In  any  Normal  Scheme,  and  therefore  approximately  in  an  observed 
one,  if  the  value  of  the  Deviation  is  given  at  any  one  specified  Grade  the 
whole  Curve  is  determined.  Let  D  he  the  given  Deviation,  and  d  the 
tabular  Deviation  at  the  same  Grade,  as  found  in  Table  8  ;  then  multiply 

every  entry  in  Table  8  ^J—r.  As  the  tabular  value  of  |J  is  1,  it  will  become 

changed  into  _. 
^  d 


62  NATURAL  INHERITANCE.  [chap. 

The  Charms  of  Statistics. — It  is  difficult  to  under- 
stand why  statisticians  commonly  limit  their  inquiries 
to  Averages,  and  do  not  revel  in  more  comprehensive 
views.  Their  souls  seem  as  dull  to  the  charm  of  variety 
as  that  of  the  native  of  one  of  our  flat  English  counties, 
whose  retrospect  of  Switzerland  was  that,  if  its  moun- 
tains could  be  thrown  into  its  lakes,  two  nuisances 
would  be  got  rid  of  at  once.  An  Average  is  but  a 
solitary  fact,  whereas  if  a  single  other  fact  be  added  to 
it,,  an  entire  Normal  Scheme,  which  nearly  corresponds 
to  the  observed  one,  starts  potentially  into  existence. 

Some  people  hate  the  very  name  of  statistics,  but  I 
find  them  full  of  beauty  and  interest.  Whenever  they 
are  not  brutalised,  but  delicately  handled  by  the  higher 
methods,  and  are  warily  interpreted,  their  power  of 
dealing  with  complicated  phenomena  is  extraordinary. 
They  are  the  only  tools  by  which  an  opening  can  be  cut 

(2)  If  the  Measures  at  any  two  specified  Grades  are  given,  the  whole 
Scheme  of  Measures  is  thereby  determined.  Let  ^,  5  be  the  two  given 
Measures  of  which  A  is  the  larger,  and  let  a,  h  be  the  values  of  the  tabular 
Deviations  for  the  same  Grades,  as  found  in  Table  8,  not  omitting  their 
signs  of  jplus  or  minus  as  the  case  may  be. 

A  —B 

Then  the  (J  of  the  Scheme  =  ± j  .  (The  sign  of  |J  is  not  to  be  re- 
garded ;  it  is  merely  a  magnitude.) 

\^  =  A  -  a^;  ot\^  =  B  -  h[^. 

Example  :        A^  situated  at  Grade  55°,  =  14*38 
B,  situated  at  Grade    5",  =    9*12 
The  corresponding  tabular  Deviations  are  : — a  =  -j-0'19;  h  —  —  2  •44. 

Therefore   R  =  '^'^^  "  ^^'^  =^^=  2-0 
^  0-19  H-  2-44       2-63 

M  =  14.38  -  0-19  X  2  =  14-0 
or  =     9-12  +  2-44  X  2  =  14*0 


v.] 


NORMAL  VARIABILITY. 


63 


through  the  formidable  thicket  of  difficulties  that  bars 
the  path  of  those  who  pursue  the  Science  of  man. 

Mechanical  Illustration  of  the  Cause  of  the  Curve  of 
Frequency. — The  Curve  of  Frequency,  and  that  of  Dis- 
tribution, are  convertible  :  therefore  if  the  genesis  of  either 
of  them  can  be  made  clear,  that  of  the  other  becomes 
also  intelligible.  I  shall  now  illustrate  the  origin  of  the 
Curve  of  Frequency,  by  means  of  an  apparatus  shown  in 
Fig.  7,  that  mimics  in  a  very  pretty  way  the  conditions 


FIG.T. 


/ 

^ 

V 

\ 

• 

• 

/ 

/ 

1 

• 

N 

15 

FIG  .8. 

A 

B 

FIG  .9. 


A 


B 


r 

1 

V 

> 

( 

c 

/ 

/ 

ft 
• 

/ 

f 

on  which  Deviation  depends.  It  is  a  frame  glazed  in 
front,  leaving  a  depth  of  about  a  quarter  of  an  inch  be- 
hind the  glass.  Strips  are  placed  in  the  upper  part  to  act 
as  a  funnel.     Below  the  outlet  of  the  funnel  stand  a 


64  NATURAL  INHERITANCE.  [chap. 

succession  of  rows  of  pins  stuck  squarely  into  tlie  back- 
board, and  below  these  again  are  a  series   of  vertical 
compartments.      A    charge   of   small    sliot   is   inclosed. 
When  the  frame  is  held  topsy-turvy,  all  the  shot  runs 
to  the  upper  end  ;  then,  when  it  is  turned  back  into 
its  working    position,    the   desired   action   commences. 
Lateral  strips,  shown  in  the  diagram,  have  the  effect  of 
directing  all  the  shot  that  had  collected  at  the  upper 
end  of  the  frame  to  run  into  the  wide  mouth  of  the 
funnel.     The  shot  passes  through  the  funnel  and  issuing 
from  its  narrow  end,  scampers  deviously  down  through 
the  pins  in  a  curious  and  interesting  way ;  each  of  them 
darting  a  step  to  the  right  or  left,  as  the  case  may  be, 
every  time  it  strikes  a  pin.     The  pins  are  disposed  in  a 
quincunx  fashion,  so  that  every  descending  shot  strikes 
against   a  pin   in   each    successive  row.      The   cascade 
issuing  from  the  funnel  broadens  as  it  descends,  and,  at 
length,  every  shot  finds  itself  caught  in  a  compartment 
immediately  after  freeing  itself  from  the  last  row  of 
pins.    The  outline  of  the  columns  of  shot  that  accumulate 
in  the    successive    compartments   approximates   to  the 
Curve  of   Frequency  (Fig.  3,  p.  38),  and  is  closely  of 
the  same  shape  however  often  the  experiment  is  re- 
peated.    The  outline  of  the  columns  would  become  more 
nearly  identical  with  the  Normal  Curve  of  Frequency, 
if  the  rows  of  pins  were  much  more  numerous,  the  shot 
smaller,  and  the  compartments  narrower ;  also  if  a  larger 
quantity  of  shot  w^as  used. 

The  principle  on  which  the   action  of  the  apparatus 
depends  is,  that  a  number  of   small  and  independent 


v.]  NORMAL  VARIABILITY.  65 

accidents  befall  each  sliot  in  its  career.  In  rare  cases, 
a  long  run  of  luck  continues  to  favour  the  course  of 
a  particular  shot  towards  either  outside  place,  but  in 
the  large  majority  of  instances  the  number  of  accidents 
that  cause  De^dation  to  the  right,  balance  in  a  greater 
or  less  degree  those  that  cause  Deviation  to  the  left. 
Therefore  most  of  the  shot  finds  its  way  into  the  com- 
partments that  are  situated  near  to  a  perpendicular  line 
drawn  from  the  outlet  of  the  funnel,  and  the  Frequency 
with  which  shots  stray  to  different  distances  to  the  right 
or  left  of  that  line  diminishes  in  a  much  faster  ratio 
than  those  distances  increase.  This  illustrates  and 
explains  the  reason  why  mediocrity  is  so  common. 

If  a  larger  quantity  of  shot  is  put  inside  the  apparatus, 
the  resulting  curve  will  be  more  humped,  but  one  half 
of  the  shot  win  stiU  faU  within  the  same  distance  as 
before,  reckoning  to  the  right  and  left  of  the  perpen- 
dicular line  that  passes  through  the  mouth  of  the 
funnel.  This  distance,  which  does  not  vary  with  the 
quantity  of  the  shot,  is  the  "  Prob  :  Error,"  or  "  Prob  : 
Deviation,"  of  any  single  shot,  and  has  the  same  value 
as  our  Q.  But  a  Scheme  of  Frequency  is  unsuitable 
for  finding  the  values  of  either  IVI  or  Q.  To  do  so,  we 
must  divide  its  strangely  shaped  area  into  four  equal 
parts  by  vertical  lines,  which  is  hardly  to  be  efi'ected 
except  by  a  tedious  process  of  "  Trial  and  Error."  On 
the  other  hand  iVI  and  Q  can  be  derived  from  Schemes 
of  Distribution  with  no  more  trouble  than  is  needed  to 
divide  a  line  into  four  equal  parts. 

F 


66  NATURAL  INHERITANCE.  [chap. 

Order  in  Apparent  Chaos. — I  know  of  scarcely  any- 
thing so  apt  to  impress  tlie  imagination  as  the  wonderful 
form  of  cosmic  order  expressed  by  the  "  Law  of  Fre- 
c|iiency  of  Error."  The  law  would  have  been  personified 
by  the  Greeks  and  deified,  if  they  had  known  of  it.  It 
reigns  v/ith  serenity  and  in  complete  self-effacement 
amidst  the  wildest  confusion.  The  huger  the  mob,  and 
the  greater  the  apparent  anarchy,  the  more  perfect  is  its 
sway.  It  is  the  supreme  law  of  Unreason.  Whenever 
a  large  sample  of  chaotic  elements  are  taken  in  hand 
and  marshalled  in  the  order  of  their  magnitude,  an  un- 
suspected and  most  beautiful  form  of  regularity  proves 
to  have  been  latent  all  along.  The  tops  of  the  mar- 
shalled row  form  a  flowing  curve  of  invariable  pro- 
portions ;  and  each  element,  as  it  is  sorted  into  place, 
finds,  as  it  were,  a  pre-ordained  niche,  accurately 
adapted  to  fit  it.  If  the  measurement  at  any  two 
specified  Grades-  in  the  row  are  known,  those  that  will 
be  found  at  every  other  Grade,  except  towards  the 
extreme  ends,  can  be  predicted  in  the  way  already 
explained,  and  with  much  precision. 

Prohlems  in  the  Lain  of  Brror. — All  the  properties  of 
the  Law  of  Frequency  of  Error  can  he  expressed  in 
terms  of  Q,  or  of  the  Prob:  Error,  just  as  those  of  a 
circle  can  be  expressed  in  terms  of  its  radius.  The 
visible  Schemes  are  not,  however,  to  be  removed  too 
soon  from  our  imagination.  It  is  always  well  to  retain 
a  clear  geometric  view  of  the  facts  when  we  are  dealing 
with  statistical  problems,  which  abound  with  dangerous 


v.]  NORMAL  VARIABILITY.  G7 

pitfalls,  easily  overlooked  by  the  unwary,  while  they  are 
cantering  gaily  along  upon  their  arithmetic.  The  Laws 
of  Error  are  beautiful  in  themselves  and  exceedingly 
fascinating  to  inquirers,  owing  to  the  thoroughness  and 
simplicity  with  which  they  deal  with  masses  of  materials 
that  appear  at  first  sight  to  be  entanglements  on  the 
largest  scale,  and  of  a  hopelessly  confused  description. 
I  will  mention  five  of  the  laws. 

(1)  The  following  is  a  mechanical  illustration  of  the 
first  of  them.  In  the  apparatus  already  described,  let  q 
stand  for  the  Prob:  Error  of  any  one  of  the  shots 
that  are  dispersed  among  the  compartments  BB  at  its 
base.  Now  cut  the  apparatus  in  two  parts,  horizontally 
through  the  rows  of  pins.  Separate  the  parts  and  interpose 
a  row  of  vertical  compartments  A  A,  as  in  Fig.  8,  p.  63, 
where  the  bottom  compartments,  BB,  corresponding  to 
those  shown  in  Fig.  7,  are  reduced  to  half  their  depth,  in 
order  to  bring  the  whole  figure  within  the  same  sized 
outline  as  before.  The  compartments  BB  are  still  deep 
enough  for  their  purpose.  It  is  clear  that  the  inter- 
polation of  the  AA  compartments  can  have  no  ultimate 
efi'ect  on  the  final  dispersion  of  the  shot  into  those  at 
BB.  Now  close  the  bottoms  of  all  the  AA  compart- 
ments ;  then  the  shot  that  falls  from  the  funnel  will  be 
retained  in  them,  and  will  be  comparatively  little  dis- 
persed. Let  the  Prob:  Error  of  a  shot  in  the  AA  com- 
partments be  called  a.  Next,  open  the  bottom  of  any 
one  of  the  AA  compartments  ;  then  the  shot  it  contains 
will  cascade  downwards  and  disperse  themselves  among 
the  BB  compartments  on  either  side  of  the  per|)endicu- 

F  2 


08  NATURAL  INHERITANCE.  [chap 

lar  line  drawn  from  its  starting  point,  and  each  sliot 
will  liave  a  Prob:  Error  tliat  we  will  call  h.  Do  this 
for  all  the  AA  compartments  in  turn  ;  h  will  be  the 
same  for  all  of  them,  and  the  final  result  must  be  to  re- 
produce the  identically  same  system  in  the  BB  com- 
partments that  was  shown  in  Fig.  7,  and  in  which  each 
shot  had  a  Prob:  Error  of  q. 

The  dispersion  of  the  shot  at  BB  may  therefore  be 
looked  upon  as  compounded  of  two  superimposed  and 
independent  systems  of  dispersion.  In  the  one,  when 
acting  singly,  each  shot  has  a  Prob:  Error  of  a  ;  in 
the  other,  when  acting  singly,  each  shot  has  a  Prob: 
Error  of  h,  and  the  result  of  the  two  acting  together  is 
that  each  shot  has  a  Prob:  Error  of  q.  What  is  the 
relation  between  a,  h,  and  q  ?  Calculation  shows  that 
q^  =  a^-\-  h^.  In  other  words,  q  corresponds  to  the  hypo- 
thenuse  of  a  right-angled  triangle  of  which  the  other  two 
sides  are  a  and  h  respectively. 

(2)  It  is  a  coroUary  of  the  foregoing  that  a  system  Z, 
in  which  each  element  is  the  Sum  of  a  couple  of  inde- 
pendent Errors,  of  which  one  has  been  taken  at  random 
from  a  Normal  system  A  and  the  other  from  a  Normal 
system  B,  will  itself  be  Normal.^  Calling  the  Q  of  the  Z 
system  q,  and  the  Q  of  the  A  and  B  systems  respectively, 
a  and  h,  then  g^  =  a^  +  h^. 

1  We  may  see  tlie  rationale  of  this  corollary  if  we  invert  part  of  the 
statement  of  the  problem.  Instead  of  saying  that  an  a  element  deviates 
from  its  m,  and  that  a  b  element  also  deviates  independently  from  its  m,  we 
may  phrase  it  thus  :  An  a  element  deviates  from  its  M,  and  its  M  deviates 
from  the  b  element.  Therefore  the  deviation  of  the  b  element  from  the 
A  element  is  compounded  of  two  independent  deviations,  as  in  Prohlem  1. 


v.]  NORMAL  VARIABILITY.  69 

(3)  Suppose  that  a  row  of  compartments,  whose  upper 
openings  are  situated  like  those  in  Fig.  7,  page  63,  arc 
made  first  to  converge  towards  some  given  point  below, 
but  that  before  reaching  it  their  sloping  course  is 
checked  and  they  are  thenceforward  allowed  to  drop 
vertically  as  in  Fig.  9.  The  effect  of  this  will  be  to 
compress  the  heaj)  of  shot  laterally ;  its  outline  will  still 
be  a  Curve  of  Frequency,  but  its  Prob:  Error  will  be 
diminished. 

The  foregoing  three  proj)erties  of  the  Law  of  Error  are 
well  known  to  mathematicians  and  require  no  demon- 
stration here,  but  two  other  properties  that  are  not 
familiar  will  be  of  use  also ;  proofs  of  them  by  ISir.  J. 
Hamilton  Dickson  are  given  in  Appendix  B.  They  are 
as  follows.  I  purposely  select  a  different  illustration  to 
that  used  in  the  Appendix,  for  the  sake  of  presenting 
the  same  general  problem  under  more  than  one  of  its 
applications. 

(4)  Bullets  are  fired  by  a  man  who  aims  at  the  centre 
of  a  target,  which  we  will  call  its  M,  and  we  will  suppose 
the  marks  that  the  bullets  make  to  be  painted  red,  for 
the  sake  of  distinction.  The  system  of  lateral  deviations 
of  these  red  marks  from  the  centre  IVI  will  be  approxi- 
mately Normal,  whose  Q  we  will  call  c.  Then  another 
man  takes  aim,  not  at  the  centre  of  the  target,  but  at 
one  or  other  of  the  red  marks,  selecting  these  at  random. 
We  will  suppose  his  shots  to  be  painted  green.  The 
lateral  distance  of  any  green  shot  from  the  red  mark 
at  which  it  was  aimed  will  have  a  Prob:  Error  that  we 


70  NATURAL  INHERITANCE.  [chap.  v. 

will  call  h.  Now,  if  the  lateral  distance  of  a  particular 
green  mark  from  IVI  is  given,  what  is  the  most  prohahle 
distance  from  IVI  of  the  red  mark  at  which  it  was  aimed  ? 

(5)  What  is  the  Prob:  Error  of  this  determination  ? 

In  other  words,  if  estimates  have  been  made  for  a  great 

many  distances  founded  upon  the  formula  in  (4),  they 

would  be  correct  on  the  average,  though  erroneous  in 

particular  cases.      The  errors  thus  made  would  form  a 

normal  system  whose  Q  it  is  desired  to  determine.     Its 

1      •           he 
value  IS  -—— ^ 

Vip'  +  c^) 

By  the  help  of  these  five  problems  the  statistics  of 
heredity  become  perfectly  manageable.  It  will  be 
found  that  they  enable  us  to  deal  with  Fraternities, 
Populations,  or  other  Groups,  just  as  if  they  were  units. 
The  largeness  of  the  number  of  individuals  in  any  of 
our  groups  is  so  far  from  scaring  us,  that  they  are  actu- 
ally welcomed  as  making  the  calculations  more  sure 
and  none  the  less  simple. 


CHAPTEE   VI. 

DATA. 

EecorJs  of  rainilj  Faculties,  or  E.  F.  F.  data. — Special  Data. — Measures 
at  my  AntLropometric  Laboratory. — Experiments  on  Sweet  Peas. 

I  HAD  to  collect  all  my  data  for  myself,  as  nothing 
existed,  so  far  as  I  know,  that  would  satisfy  even  my 
primary  requirement.  This  was  to  obtain  records  of  at 
least  two  successive  generations  of  some  population  of 
considerable  size.  They  must  have  lived  under  con- 
ditions that  were  of  a  usual  kind,  and  in  which  no  great 
varieties  of  nurture  were  to  be  found.  Natural  selection 
must  have  had  little  influence  on  the  characteristics 
that  were  to  be  examined.  These  must  be  measurable, 
variable,  and  fairly  constant  in  the  same  individual. 
The  result  of  numerous  inquiries,  made  of  the  most 
competent  persons,  was  that  I  began  my  experiments 
many  years  ago  on  the  seeds  of  sweet  peas,  and  that 
at  the  present  time  I  am  breeding  moths,  as  will  be 
explained  in  a  later  chapter,  but  this  book  refers  to 
a  human  population,  which,  take  it  all  in  all,  is  the 
easiest  to  work  with  when  the  data  are  once  ol:>tained, 


72  NATURAL  INHERITANCE.  [chap. 

to  say  notliing  of  its  being  more  interesting  by  far  than 
one  of  sweet  peas  or  of  moths. 

Record  of  Family  Faculties,  or  R.F.F.  Data. — The 
source  from  which  the  larger  part  of  my  data  is  derived 
consists  of  a  valuable  collection  of  "  Kecords  of  Family 
Faculties,"  obtained  through  the  offer  of  prizes.  They 
have  been  much  tested  and  cross-tested,  and  have  borne 
the  ordeal  very  fairly,  so  far  as  it  has  been  applied.  It 
is  well  to  reprint  the  terms  of  the  published  offer,  in 
order  to  give  a  just  idea  of  the  conditions  under  which 
they  were  compiled.     It  was  as  follows  : 

''  Mr.  Francis  Galton  offers  500^.  in  prizes  to  those 
British  Subjects  resident  in  the  United  Kingdom  who 
shall  furnish  him  before  May  15,  1884,  with  the  best 
Extracts  from  theii*  own  Family  Eecords. 

"  These  Extracts  will  be  treated  as  confidential  docu- 
ments, to  be  used  for  statistical  purposes  only,  the 
insertion  of  names  of  persons  and  places  being  required 
solely  as  a  guarantee  of  authenticity  and  to  enable  Mr. 
Galton  to  communicate  with  the  writers  in  cases  where 
further  question  may  be  necessary. 

"  The  value  of  the  Extracts  will  be  estimated  by  the 
degree  in  which  they  seem  likely  to  facilitate  the  scien- 
tific investigations  described  in  the  preface  to  the 
'Eecord  of  Family  Faculties.' 

"  More  especially : 

"  (a)  By  including  every  direct  ancestor  who  stands 
within  the  limits  of  kinship  there  specified. 

"  (6)  By  including  brief  notices  of  the  brothers  and 


vl]  data.  73 

sisters  (if  any)  of  each  of  tliose  ancestors.  (Importance 
will  be  attached  both  to  the  completeness  with  which 
each  family  of  brothers  and  sisters  is  described,  and  also 
to  the  number  of  persons  so  described.) 

"  (c)  By  the  character  of  the  evidence  upon  which  the 
information  is  based. 

"  (d)  By  the  clearness  and  conciseness  with  Y/hich  the 
statements  and  remarks  are  made. 

"  The  Extracts  must  be  legibly  entered  either  in  the 
tabular  forms  contained  in  the  copy  of  the  '  Record  of 
Family  Faculties '  (into  which,  if  more  space  is  wanted, 
additional  pages  may  be  stitched),  or  they  may  be 
written  in  any  other  book  with  pages  of  the  same  size 
as  those  of  the  Record,  provided  that  the  information  be 
arranged  in  the  same  tabular  form  and  order.  (It  will 
be  obvious  that  uniformity  in  the  arrangement  of  docu- 
ments is  of  primary  importance  to  those  who  examine 
and  collate  a  large  number  of  them.) 

"  Each  competitor  must  furnish  the  name  and  address 
of  a  referee  of  good  social  standing  (magistrate,  clergy- 
man, lawyer,  medical  practitioner,  &c.),  who  is  personally 
acquainted  with  his  family,  and  of  whom  inquiry  may 
be  made,  if  desired,  as  to  the  general  trustworthiness  of 
the  competitor. 

"  The  Extracts  must  be  sent  prepaid  and  by  post, 
addressed  to  Francis  Galton,  42  Rutland  Gate,  London, 
S.W.  It  will  be  convenient  if  the  letters  '  R.F.F.' 
(Record  of  Family  Faculties)  be  written  in  the  left- 
hand  corner  of  the  parcel,  below  the  address. 


74  NATURAL  INHERITANCE.  [chap. 

"  The  examination  will  be  conducted  by  tlie  donor  of 
tlie  prizes,  aided  by  competent  examiners. 

"  The  value  of  the  individual  prizes  cannot  be  fixed 
beforehand.  No  prize  will,  however,  exceed  5.0/.,  nor  be 
less  than  5l.,  and  500/.  will  on  the  whole  be  awarded. 

''  A  list  of  the  gainers  of  the  prizes  will  be  posted 
to  each  of  them.  It  will  be  published  in  one  or  more 
of  the  daily  newspapers,  also  in  at  least  one  clerical,  and 
one  medical  Journal." 

The  number  of  Family  Eecords  sent  in  reply  to  this 
offer,  that  deserved  to  be  seriously  considered  before 
adjudging  the  prizes,  barely  reached  150  ;  70  of  these 
being  contributed  by  males,  80  by  females.  The  re- 
mainder were  imperfect,  or  they  were  marked  "  not  for 
competition,"  but  at  least  10  of  these  have  been  to  some 
degree  utilised.  The  150  Records  were  contributed 
by  persons  of  very  various  ranks.  After  classing  the 
female  writers  according  to  the  profession  of  their 
husbands,  if  they  were  married,  or  according  to  that  of 
their  fathers,  if  they  were  unmarried,  I  found  that  each 
of  the  following  7  classes  had  20  or  somewhat  fewer 
representatives  :  (l)  Titled  persons  and  landed  gentry ; 
(2)  Army  and  Navy ;  (3)  Church  (various  denomina- 
tions) ;  (4)  Law ;  (5)  Medicine ;  (6)  Commerce,  higher 
class ;  (7)  Commerce,  lower  class.  This  accounts  for 
nearly  130  of  the  writers  of  the  Eecords ;  the  remainder 
are  land  agents,  farmers,  artisans,  literary  men,  school- 
masters, clerks,  students,  and  one  domestic  servant  in  a 
family  of  position. 


VI.]  DATA.  75 

Three  cases  occurred  in  which  the  Records  sent  by 
different  contributors  overlapped.  The  details  are 
complicated,  and  need  not  be  described  here,  but  the 
result  is  that  five  persons  have  been  adjudged  smaller 
prizes  than  they  individually  deserved. 

Every  one  of  the  replies  refers  to  a  very  large  number 
of  persons,  as  will  easily  be  understood  if  the  fact  is 
borne  in  mind  that  each  individual  has  2  parents,  4 
grandparents,  and  8  great  parents;  also  that  he  and 
each  of  those  14  progenitors  had  usually  brothers  and 
sisters,  who  were  included  in  the  incjuiry.  The  replies 
were  unequal  in  merit,  as  might  have  been  expected,  but 
many  were  of  so  high  an  order  that  I  could  not  justly 
select  a  few  as  recipients  of  large  prizes  to  the  exclusion 
of  the  rest.  Therefore  I  divided  the  sum  into  two 
considerable  groups  of  small  prizes,  all  of  which  were 
well  deserved,  regretting  much  that  I  had  none  left  to 
award  to  a  few  others  of  nearly  ecjual  merit  to  some 
of  those  who  had  been  successful.  The  list  of  winners 
is  reproduced  below,  the  four  years  that  have  elapsed 
have  of  course  made  not  a  few  changes  in  the  addresses, 
which  are  not  noticed  here. 

LIST   OF  AWAEDS. 

A  Prize  of  £1  was  awarded  to  each  op  the  40  following 

Contributors. 

Amphlett,  Jolin,  Clent,  Stourbridge  ;  Batchelor,  Mrs.  Jacobstow  Kectory, 
Stratton,  N.  Devon  ;  Bathnrst,  Miss  K.,  Vicarage,  Biggleswade,  Bedford- 
sliire  ;  Beane,  Mrs.  C.  F.,  3  Portland  Place,  Venner  Eoad,  Sydenham  ; 
Berisford,  Samuel,  Park  Villas,  Park  Lane,  Macclesfield  ;  Carruthers,  Mrs., 
Briglitside,  North  Finchley ;  Carter,  Miss  Jessie  E.,  Hazelwood,  The  Park, 
Cheltenham  ;   Cay,   Mrs.,   Eden   House,   Holyhead ;   Clark,   J.  Edmund, 


76  NATURAL  INHERITANCE.  [chap. 

I'eversham  Terrace,  York ;  Oust,  Lady  Elizabetli,  13  Eccleston  Square,  S.W. ; 
Fry,  Edward,  Portsmouth,  5  The  Grove,  Highgate,  N. ;  Gibson,  G.  A.,  M  D., 
1  Eandolph  Cliff,  Edinburgh  ;  Gidley,  B.  Conrtenay,  17  Ribblesdale  Road, 
Hornsey,  N.  ;  Gillespie,  Franklin,  M.D.,  1  The  Grove,  Aldershot  ;  Griffith- 
Boscawen,  Mrs.,  Trevalyn  Hall,  AVrexham  ;  Hard  castle,  Henry,  38  Eaton 
Square,  S.W.  ;  Harrison,  Miss  Edith,  68  Gloucester  Place,  Portman  Square, 
W.  ;  Hobhouse,  Mrs.  4  Kensington  Square,  W.  ;  Holland,  INIiss,  Ivynieath, 
Snodland,  Kent ;  Ilollis,  George,  Dartmouth  House,  Dartmouth  Park  Hill, 
N.  ;  Ingram,  Mrs.  Ades,  Chailey,  Lewis,  Sussex  ;  Johnstone,  Miss  C.  L., 
3  Clarendon  Place,  Leamington  ;  Lane-Poole,  Stanley,  6  Park  Villas  East, 
Richmond,  Middlesex  ;  Leathley,  D.  W.  B.,  59  Lincoln's  Inn  Fields  (in 
trast  for  a  competitor  who  desires  her  name  not  to  be  published)  ;  Lewin, 
Lieutenant-Colonel  T.  H.,  Colway  Lodge,  Lyme  Regis ;  Lipscomb,  R.  H., 
East  Buclleigh,  Budleigh  Salterton,  Devon  ;  Maiden,  Henry  C,  Wincllesham 
House,  Brighton ;  Maiden,  Henry  Elliot,  Kitland,  Holmwood,  Surrey ; 
McCall,  Hardy  Bertram,  5  St.  Augustine's  Road,  Edgbaston,  Birmingham  ; 
Moore,  Miss  Georgina  M.,  45  Chepstow  Place,  Bayswaler,  AV. ;  Newlands, 
Mrs.,  Raeden,  near  Aberdeen ;  Pearson,  David  R.,  M.D.,  23  Upper  Phili- 
more  Place,  Kensington,  W.  ;  Pearson,  Mrs.,  The  Garth,  Woodside  Park, 
North  Finchley  :  Pechell,  Hervey  Charles,  6  West  Chapel  Street,  Curzon 
Street,  W.  ;  Roberts,  Samuel,  21  Roland  Gardens,  S.W.  ;  Smith,  Mrs. 
Archibald,  Riverbank,  Putney,  S.W. ;  Strachey,  Mrs.  Fowey  Lodge, 
Clapham  Common,  S.W.  ;  Sturge,  Miss  Mary  C,  Chilliswood,  Tyndall's 
Park,  Bristol ;  Sturge,  Mrs.  R.  F.,  101  Pembroke  Road,  Clifton  ;  Wilson, 
Edward  T.,  M.D.,  Westall,  Cheltenham. 

A  Prize  of  £b  was  awarded  to  each  of  the  44  following 

Contributors. 

Allan,  Francis  J.,  M.D.,  1  Dock  Street,  E.  ;  Atkinson,  Mrs.,  Clare  College 
Lodge,  Cambridge  ;  Bevan,  Mrs ,  Plumpton  House,  Bury  St.  Edmunds  ; 
Browne,  Miss,  Maidenwell  House,  Louth,  Lincolnshire  ;  Cash,  Frederick 
Goodall,  Gloucester  ;  Chisholm,  Mrs.,  Church  Lane  House,  Haslemere, 
Surrey ;  Collier,  Mrs.  R.,  7  Thames  Embankment,  Chelsea ;  Croft,  Sir 
Herbert  G.  D.,  Lugwardine  Court,  Hereford  ;  Davis,  Mrs.  (care  of  Israel 
Davis,  6  King's  Bench  Walk,  Temple,  E.G.)  ;  Drake,  Henry  H.,  The 
Firs,  Lee,  Kent;  Ercke,  J.  J.  G.,  13,  Brownhill  Road,  Catford,  S.E.  ; 
Flint,  Fenner  Ludd,  83  Brecknock  Eoad,  N.  ;  Ford,  William,  4  South 
Square,  Gray's  Inn,  W.C.  ;  Foster,  Rev.  A.  J.,  The  Vicarage,  Wootton, 
Bedford  ;  Glanville-Richards,  AV.  V.  S.,  23  Endsleigh  Place,  Plymouth  ; 
Hale,  C.  D.  Bowditch,  8  Sussex  Gardens,  Hyde  Park,  W.  ;  Horder,  Mrs. 
Mark,  Rothenwood,  Ellen  Grove,  Salisbury  ;  Jackson,  Edwin,  79  Withington 
Road,  Whalley  Range,  Manchester  ;  Jackson,  George,  1  St.  George's  Terrace, 
Plymouth  ;  Kesteven,  W.   H.,  401   Holloway  Road,  N.  ;  Lawrence,   Mrs. 


VI.]  DATA.  77 

Alfred,  16  Suffolk  Square,  Cheltenham  ;  Lawrie,  Mrs.,  1  Chesham  Place, 
S.W.  ;  Leveson-Gower,  G.  W.  G.,  Titsey  Place,  Limpsfield,  Surrey  ;  Lobb, 
H.  W.,  66  Eussell  Square,  W.  ;  McConnell,  Miss  M.  A.  Brooklands, 
Prestwich,  Manchester ;  Marshall,  Mrs.,  Fenton  Hall,  Stoke-upon-Trent  ; 
Meyer,  Mrs.,  1  Rodney  Place,  Clifton,  Bristol;  Milman,  Mrs.,  The  Governor's 
House,  H.M.  Prison,  Camden  Road  ;  Olding,  Mrs.  W.  4  Brunswick  Road, 
Brighton,  Sussex  ;  Passingham,  Mrs.,  Milton,  Cambridge  ;  Pringle,  Mrs. 
Fairnalie,  Fox  Grove  Road,  Beckenham,  Kent ;  Reeve,  Miss,  Foxholes, 
Christchurch,  Hants ;  Scarlett,  Mrs.,  Boscorab  Manor,  Bournemouth  ; 
Shand,  William,  57  Caledonian  Road,  N. ;  Shaw,  Cecil  E.,  Wellington 
Park,  Belfast ;  Sizer,  Miss  Kate  T.,  Moorlands,  Great  Huntley,  Colchester ; 
Smith,  Miss  A.  M.  Carter,  Thistleworth,  Stevenage  ;  Smith,  Rev.  Edward  S., 
Yiney  Hall  Vicarage,  Blakeney,  Gloucestershire  ;  Smith,  Mrs.  F,  P.,  Cliffe 
House,  Sheffield ;  Staveley,  Edw.  S.  R.,  Mill  Hill  School,  N.W. ;  Slurge, 
Miss  Mary  W.,  17  Frederick  Road,  Eclgbaston,  Birmingham  ;  Terry,  Mrs., 
Tostock,  Bury  St.  Edmunds,  Suffolk;  Utley,  W,  H.  Alliance  Hotel, 
Cathedral  Gates,  Manchester  ;  Weston,  Mrs.  Ensleigh,  Lansdown,  Bath  ; 
Wodehouse,  Mrs.  E.  R.  50  Chester  Square,  S.W. 


The  material  in  these  Eecords  is  sufficiently  varied  to 
be  of  service  in  many  inquiries.  The  chief  subjects  to 
which  allusion  will  be  made  in  this  book  concern 
Statnre,  Eye-Colonr,  Temper,  the  Artistic  Faculty,  and 
some  forms  of  Disease,  but  others  are  utilized  that  refer 
to  Marriage  Selection  and  Fertility. 

The  following  remarks  in  this  Chapter  refer  almost 
wholly  to  the  data  of  Stature. 

The  data  derived  from  the  Eecords  of  Family  Faculties 
will  be  hereafter  distinguished  by  the  letters  R.F.F.  I 
was  able  to  extract  from  them  the  statures  of  205  couples 
of  parents,  with  those  of  an  aggregate  of  930  of  their 
adult  children  of  both  sexes.  I  must  repeat  that  when 
dealing  with  the  female  statures,  I  transmuted  them  to 
their  male  equivalents ;  and  treated  them  when  thus 
transmuted,  on  equal  terms  with  the  measures  of  males. 


78  NATURAL  INHERITANCE.  [chap. 

except  where  otherwise  expressed.  The  factor  I  used 
was  1*08,  which  is  equivalent  to  adding  a  little  less  than 
one-twelfth  to  each  female  height.  It  differs  slightly 
from  the  factors  employed  by  other  anthropologists, 
who,  moreover,  differ  a  trifle  between  themselves ;  any- 
how, it  suits  my  data  better  than  1*07  or  1*09.  I  can 
say  confidently  that  the  final  result  is  not  of  a  kind  to 
be  sensibly  affected  by  these  minute  details,  because  it 
happened  that  owing  to  a  mistaken  direction,  the  com- 
puter to  whom  I  first  entrusted  the  figures  used  a 
somewhat  different  factor,  yet  the  final  results  came  out 
closely  the  same.  These  E.F.F.  data  have  by  no  means 
the  precision  of  the  observations  to  be  spoken  of  in  the 
next  paragraph.  In  many  cases  there  remains  consider- 
able doubt  whether  the  measurement  refers  to  the  height 
with  the  shoes  on  or  off;  not  a  few  of  the  entries  are,  I 
fear,  only  estimates,  and  the  heights  are  commonly  given 
only  to  the  nearest  inch.  StiU,  speaking  from  a  know- 
ledge of  many  of  the  contributors,  I  am  satisfied  that  a 
fair  share  of  these  returns  are  undoubtedly  careful  and 
thoroughly  trustworthy,  and  as  there  is  no  sign  or  sus- 
picion of  bias,  I  have  reason  to  place  confidence  in  the 
values  of  the  Means  that  are  derived,  from  them.  They 
bear  the  internal  tests  that  have  been  appHed  better 
than  might  have  been  expected,  and  when  checked  by 
the  data  described  in  the  next  paragraph,  and  cautiously 
treated,  they  are  very  valuable. 

Special  Data. — A  second  set  of  data,  distinguished 
by   the  name    of   "  Sj^ecial   observations,"   concern  the 


VI.]  DATA.  79 

variations  in  stature  amona;  Brothers.  I  circulated  cards 
of  inquiry  among  trusted  correspondents,  stating  that  I 
wanted  records  of  the  heights  of  brothers  who  were  more 
than  24  and  less  than  60  years  of  age ;  that  it  was 
not  necessary  to  send  the  statures  of  all  of  the  brothers 
of  the  same  family,  but  only  of  as  many  of  them  as 
could  be  easily  and  accurately  measured,  and  that  the 
height  of  even  two  brothers  would  be  acceptable.  The 
blank  forms  sent  to  be  filled,  were  ruled  vertically  in 
three  parallel  columns :  (a)  family  name  of  each  set  of 
brothers  ;  (b)  order  of  birth  in  each  set ;  (c)  height 
without  shoes,  in  feet  and  inches.  A  place  was  reserved 
at  the  bottom  for  the  name  and  address  of  the  sender. 
The  circle  of  inquirers  widened,  but  I  was  satisfied  when 
I  had  obtained  returns  of  295  families,  containing  in 
the  aggregate  783  brothers,  some  few  of  whom  also 
appear  in  the  E.F.F.  data.  Though  these  two  sets  of 
returns  overlap  to  a  trifling  extent,  they  are  practically 
independent.  I  look  upon  the  "  Special  Observations  " 
as  being  quite  as  trustworthy  as  could  be  expected  in  any 
such  returns.  They  bear  every  internal  test  that  I  can 
apply  to  them  in  a  very  satisfactory  manner.  The  mea- 
sures are  commonly  recorded  to  quarter  or  half  inches. 

Measures  at  my  Anthropometric  Laboratory. — A 
third  set  of  data  have  been  incidentally  of  service. 
They  are  the  large  lists  of  measures,  nearly  10,000  in 
number,  made  at  my  Anthropometric  Laboratory  in  the 
International  Health  Exhibition  of  1884. 

4.  Experiments  on  Sweet  Peas. — The  last  of  the  data 


80  NATURAL  INHERITANCE.  [chap. 

that  I  need  specify  were  the  very  first  that  I  used  ;  they 
refer  to  the  sizes  of  seeds,  which  are  equivalent  to  the 
Statures  of  seeds.  I  both  measured  and  weighed  them, 
but  after  assuring  myself  of  the  equivalence  of  the 
two  methods  (see  Appendix  C),  confined  myself  to 
ascertaining  the  weights,  as  they  were  much  more 
easily  ascertained  than  the  measures.  It  is  more 
than  10  years  since  I  procured  these  data.  They 
were  the  result  of  an  extensive  series  of  experiments 
on  the  produce  of  seeds  of  difi'erent  sizes, .  but  of 
the  same  species,  conducted  for  the  following  reasons. 
I  had  endeavoured  to  find  a  population  possessed 
of  some  measurable  characteristic  that  was  suitable 
for  investigating  the  causes  of  the  statistical  similarity 
between  successive  generations  of  a  people,  as  will  here- 
after be  discussed  in  Chapter  YIII.  At  last  I  determined 
to  experiment  on  seeds,  and  after  much  inquiry  of  very 
competent  advisers,  selected  sweet-peas  for  the  purpose. 
They  do  not  cross-fertilize,  which  is  a  very  exceptional 
condition  among  plants ;  they  are  hardy,  prolific,  of  a 
convenient  size  to  handle,  and  nearly  spherical ;  their 
weight  does  not  alter  perceptibly  when  the  air  changes 
from  damp  to  dry,  and  the  little  pea  at  the  end  of  the 
pod,  so  characteristic  of  ordinary  peas,  is  absent  in  sweet- 
peas.  I  began  by  weighing  thousands  of  them  individ- 
ually, and  treating  them  as  a  census  ofiicer  would  treat 
a  large  population.  Then  I  selected  with  great  pains 
several  sets  for  planting.  Each  set  contained  seven 
little  packets,  numbered  K,  L,  M,  N,  0,  P,  and  Q, 
each  of  the  seven  packets  contained  ten  seeds  of  almost 


VI.]  DATA.  81 

exactly  the  same  weight ;  those  in  K  being  the  heaviest, 
L  the  next  heaviest,  and  so  down  to  Q,  which  was  the 
lightest.  The  precise  weights  are  given  in  Appendix  C, 
together  with  the  corresponding  diameters,  which  I 
ascertained  by  laying  100  peas  of  the  same  weight  in  a 
row.  The  weights^  rim  in  an  arithmetic  series,  ha^dng  a 
common  average  difference  of  0*172  grain.  I  do  not  of 
course  profess  to  work  to  thousandths  of  a  grain,  though 
I  did  work  to  somewhat  less  than  one  hundredth  of  a 
grain  ;  therefore  the  third  decimal  place  represents  little 
more  than  an  arithmetical  working  value  which  has  to  be 
regarded  in  multiplications,  lest  an  error  of  sensible  im- 
portance should  be  introduced  by  its  neglect.  Curiously 
enough,  the  diameters  were  found  also  to  run  approxi- 
mately in  an  arithmetic  series,  owing,  I  suppose,  to  the 
misshape  and  corrugations  of  the  smaller  seeds,  which 
gave  them  a  larger  diameter  than  if  they  had  been 
plumped  out  into  spheres.  AH  this  is  shown  in  the 
Appendix,  where  it  will  be  seen  that  T  was  justified 
in  sorting  the  seeds  by  the  convenient  method  of  the 
balance  and  weights,  and  of  accepting  the  weights  as 
directly  proportional  to  the  mean  diameters. 

In  each  experiment,  seven  beds  were  prepared  in 
parallel  rows ;  each  was  1^  feet  wide  and  5  feet 
long.  Ten  holes  of  1  inch  deep  were  dibbled  at  equal 
distances  apart  along  each  bed,  and  a  single  seed  was 
put  into  each  hole.  The  beds  were  then  bushed  over  to 
keep  off  the  birds.  Minute  instructions  were  given  to 
ensure  uniformity,  which  I  need  not  repeat  here.  The 
end  of  all  was  that  the  seeds  as  they  became  ripe  were 

G 


82  NATURAL  INHERITANCE.  [chap.  vi. 

collected  from  time  to  time  and  put  into  bags  that  I 
had  sent,  lettered  from  K  to  Q,  the  same  letters  having 
been  stuck  at  the  ends  of  the  beds.  When  the  crop  was 
coming  to  an  end,  the  whole  remaining  produce  of  each 
bed,  including  the  foliage,  was  torn  up,  tied  together, 
labelled,  and  sent  to  me.  Many  friends  and  acquaint- 
ances had  each  undertaken  the  planting  and  culture  of 
a  complete  set,  so  that  I  had  simultaneous  experiments 
going  on  in  various  parts  of  the  United  Kingdom  from 
Nairn  in  the  North  to  Cornwall  in  the  South.  Two 
proved  failures,  but  the  final  result  was  that  I  obtained 
the  more  or  less  complete  produce  of  seven  sets ;  that  is 
to  say,  the  produce  of  7x7x10,  or  of  490  carefully 
weighed  parent  seeds.  Some  additional  account  of  the 
results  is  given  in  Appendix  C. 

It  would  be  wholly  out  of  place  to  enter  here  into 
further  details  of  the  experiments,  or  to  narrate  the 
numerous  little  difiiculties  and  imperfections  I  had  to 
contend  with,  and  how  I  balanced  doubtful  cases  ;  how 
I  divided  returns  into  groups  to  see  if  they  confirmed 
one  another,  or  how  I  conducted  any  other  w^ell-known 
statistical  operation.  Sufiice  it  to  say  that  I  took  im- 
mense pains,  which,  if  I  had  understood  the  general 
conditions  of  the  ^^I'o^^lem  as  clearly  as  I  do  now,  I 
should  not  perhaps  have  cared  to  bestow.  The  results 
were  most  satisfactory.  They  gave  me  two  data,  which 
were  all  that  I  wanted  in  order  to  understand  in  its 
simplest  approximate  form,  the  way  in  which  one 
generation  of  a  people  is  descended  from  a  previous  one  ; 
and  thus  I  got  at  the  heart  of  the  problem  at  once. 


CHAPTER  YIL 

DISCUSSION   OF   THE   DATA    OF   STATUTE. 

Stature  as  a  subject  for  inquiry, — Marriage  Selection. — Issue  of  unlike 
Parents. — Description  of  the  Tables  of  Stature.  Mid-Stature  of  tbe 
Population. — Variability  of  the  Population. — Variability  of  Mid- 
Parents. — Variability  in  Co-Fraternities. — Regression  :  «,  Filial  ; 
6,  Mid-Parental  ;  c,  Parental ;  d^  Fraternal. — Squadrons  of  Statures. — 
Successive  Generations  of  a  People. — Natural  Selection. — Variability 
in  Fraternities. — Trustworthiness  of  tlie  Constants. — General  view  of 
Kinship. — Separate  Contribution  from  each  Ancestor. — Pedigree 
Lloths. 

Stature  as  a  Subject  for  Inquiry. — The  first  of  these 
inquiries  into  the  laws  of  human  heredity  deals  with 
hereditary  Stature,  which  is  an  excellent  subject  for 
statistics.  Some  of  its  merits  are  obvious  enough,  such 
as  the  ease  and  frequency  with  which  it  may  be  measured, 
its  practical  constancy  during  thirty-five  or  forty  years 
of  middle  life,  its  comparatively  small  dependence  upon 
clifi'erences  of  bringing  up,  and  its  inconsiderable  influ- 
ence on  the  rate  of  mortalitv.  Other  advantaQ;es  which 
are  not  equally  obvious  are  equally  great.  One  of  these 
is  due  to  the  fact  that  human  stature  is  not  a  simple 
element,    but   a    sum    of  the    accumidated   lengths    or 

G  2 


Si  NATURAL  INHERITANCE.  [chap. 

thicknesses  of  more  than  a  hnndred  iDoclily  parts,  each 
so  distinct  from  the  rest  as  to  have  earned  a  name  by 
which  it  can  be  s|)ecified.  The  list  includes  about  fifty 
separate  bones,  situated  in  the  skull,  the  spine,  the 
pelvis,  the  two  legs,  and  in  the  two  ankles  and  feet. 
The  bones  in  both  the  lower  limbs  have  to  be  counted, 
because  the  Stature  depends  upon  their  average  length. 
The  two  cartilages  interposed  between  adjacent  bones, 
wherever  there  is  a  movable  joint,  and  the  single 
cartilage  in  other  cases,  are  rather  more  numerous  than 
the  bones  themselves.  The  fleshy  parts  of  the  scalp 
of  the  head  and  of  the  soles  of  the  feet  conclude  the 
list  Account  should  also  be  taken  of  the  shape  and 
set  of  the  many  bones  which  conduce  to  a  more  or  less 
arched  instep,  straight  back,  or  high  head.  I  noticed 
in  the  skeleton  of  O'Brien,  the  Irish  giant,  at  the  College 
of  Surgeons,  which  is  the  tallest  skeleton  in  any  English 
museum,  that  his  great  stature  of  about  7  feet  7  inches 
would  have  been  a  trifle  increased  if  the  faces  of  his 
dorsal  vertebrae  had  been  more  parallel  than  they  are, 
and  his  back  consequently  straighter. 

This  multiplicity  of  elements,  whose  variations  are  to 
some  degree  independent  of  one  another,  some  tending 
to  lengthen  the  total  stature,  others  to  shorten  it, 
corresponds  to  an  equal  number  of  sets  of  rows  of 
pins  in  the  apparatus  Fig.  7,  p.  63,  by  which  the  cause 
of  variability  was  illustrated.  The  larger  the  number  of 
these  variable  elements,  the  more  nearly  does  the  varia- 
bility of  their  sum  assume  a  "Normal"  character,  though 
the  approximation  increases  only  as  the  sc[uare  root  of 


VII.J  DISCUSSION  OF  THE  DATA  OF  STATURE.  85 

their  number.  The  beautiful  regularity  in  the  Statures  of 
a  population,  whenever  they  are  statistically  marshalled 
in  the  order  of  their  heights,  is  due  to  the  number 
of  variable  and  quasi-independent  elements  of  which 
Stature  is  the  sum. 

Mai^riage  Selection. — Whatever  may  be  the  sexual 
preferences  for  similarity  or  for  contrast,  I  find  little 
indication  in  the  average  results  obtained  from  a  fairly 
large  number  of  cases,  of  any  single  measurable  personal 
peculiarity,  whether  it  be  stature,  temper,  eye-colour, 
or  artistic  tastes,  in  influencing  marriage  selection  to 
a  notable  degree.  Nor  is  this  extraordinary,  for  though 
people  may  fall  in  love  for  trifles,  marriage  is  a  serious 
act,  usually  determined  by  the  concurrence  of  numerous 
motives.  Therefore  we  could  hardly  expect  either 
shortness  or  tallness,  darkness  or  lightness  in  com- 
plexion, or  any  other  single  quality,  to  have  in  the 
long  run  a  large  separate  influence. 

I  was  certainly  surprised  to  find  how  imperceptible 
was  the  influence  that  even  good  and  bad  Temper 
seemed  to  exert  on  marriage  selection.  A  list  was  made 
(see  Appendix  D)  of  the  observed  frequency  of  marriages 
between  persons  of  each  of  the  various  classes  of  Temper, 
in  a  group  of  111  couples,  and  I  calculated  what  would 
have  been  the  relative  frequency  of  intermarriages  be- 
tween persons  of  the  various  classes,  if  the  same  number 
of  males  and  females  had  been  paired  at  random.  The 
result  showed  that  the  observed  list  agreed  closely  with 
the  calculated  list,  and  therefore  that  these  observations 


86  NATURAL  INHERITANCE.  [chap. 

gave  no  evidence  of  discriminative  selection  in  respect 
to  Temper.  The  good-tempered  husbands  were  46  per 
cent,  in  number,  and,  between  them,  they  married  22 
good-tempered  and  24  bad-tempered  wives ;  whereas 
calculation,  having  regard  to  the  relative  proportions 
of  good  and  bad  TemjDer  in  the  two  sexes,  gave  the 
numbers  as  25  and  21.  Again,  the  bad-tempered  hus- 
bands, who  were  54  per  cent,  in  number,  married  31 
good-tempered  and  23  bad-tempered  wives,  whereas 
calculation  gave  the  number  as  30  and  24.  This  rough 
summary  is  a  just  expression  of  the  results  arrived  at 
by  a  more  minute  analysis,  which  is  described  in  the 
Appendix,  and  need  not  be  repeated  here. 

Similarly  as  regards  Eye-Colour.  If  we  analyse  the 
marriages  between  the  78  couples  whose  eye-colours  are 
described  in  Chapter  YIIL,  and  compare  the  observed 
results  with  those  calculated  on  the  supposition  that 
Eye-Colour  has  no  influence  whatever  in  marriage 
selection,  the  two  lists  will  be  found  to  be  much  alike. 
Thus  where  both  of  the  parents  have  eyes  of  the  same 
colour,  whether  they  be  light,  or  hazel,  or  dark,  the 
percentage  results  are  almost  identical,  being  37,  3,  and 
8  as  observed,  against  37,  2,  and  7  calculated.  Where 
one  parent  is  hazel-eyed  and  the  other  dark-eyed,  the 
marriages  are  as  5  observed  against  7  calculated.  But 
the  results  run  much  less  well  together  in  the  other  two 
possible  combinations,  for  where  one  parent  is  light  and 
the  other  hazel-eyed,  they  give  23  observed  against  15 
calculated ;  and  where  one  parent  is  light  and  the  other 
dark-eyed,  they  give  24  observed  against  32  calculated. 


VII.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  87 

The  effect  of  Artistic  Taste  on  marriage  selection  is 
discussed  in  Chapter  X.,  and  this  also  is  shown  to  be 
small.  The  influence  on  the  race  of  Bias  in  Marriage 
Selection  will  be  discussed  in  that  chapter. 

I  have  taken  much  trouble  at  different  times  to 
determine  whether  Stature  plays  any  sensible  part  in 
marriage  selection.  I  am  not  yet  prepared  to  offer 
complete  results,  but  shall  confine  my  remarks  for  the 
present  to  the  particular  cases  with  which  we  are  now 
concerned.  The  shrewdest  test  is  to  proceed  under  the 
guidance  of  Problem  2,  page  68.  I  find  the  Q  of 
Stature  among  the  male  population  to  be  1*7  inch, 
and  similarly  for  the  transmuted  statures  of  the  female 
population.  Consequently  if  the  men  and  (transmuted) 
women  married  at  random  so  far  as  stature  was  con- 
cerned, the  Q  in  a  group  of  couples,  each  couple 
consisting  of  a  pair  of  summed  statures,  would  be 
\/2i  X  1"7  inches  ==2*41  inches.  Therefore  the  Q  in  a 
group  of  which  each  element  is  the  mean  stature  of  a 
couple,  would  be  half  that  amount,  or  1'20  inch.  This 
closely  corresponds  to  what  I  derived  from  the  data 
contained  in  the  first  and  in  the  last  column  but  one 
of  Table  11.  The  word  "  Mid-Parent,"  in  the  headings 
to  those  columns,  expresses  an  ideal  person  of  composite 
sex,  whose  Stature  is  half  way  between  the  Stature  of 
the  father  and  the  transmuted  Stature  of  the  mother.  I 
therefore  conclude  that  marriage  selection  does  not  pay 
such  regard  to  Stature,  as  deserves  being  taken  into 
account  in  the  cases  with  which  we  are  concerned. 

I  tried  the  question  in  another  but  ruder  way,  l^y 


88  NATURAL  INHERITANCE.  [chap. 

dividing  (see  Table  9)  the  male  and  female  parents  re- 
spectively into  three  nearly  equal  groups,  of  tall,  medium, 
and  short.  It  was  impracticable  to  make  them  precisely 
equal,  on  account  of  the  roughness  with  Avhich  the 
measurements  were  recorded,  so  I  framed  rules  that 
seemed  best  adapted  to  the  case.  Consequently  the 
numbers  of  the  tall  and  short  proved  to  be  only  ap- 
proximately and  not  exactly  equal,  and  the  two  together 
were  only  approximately  equal  to  the  medium  cases. 
The  final  results  were  : — 32  instances  where  one  parent 
was  short  and  the  other  tall,  and  27  where  both  were 
short  or  both  were  tall.  In  other  words,  there  were  32 
cases  of  contrast  in  marriage,  to  27  cases  of  likeness. 
I  do  not  regard  this  difference  as  of  consequence, 
because  the  numbers  are  small,  and  because  a  slight 
change  in  the  limiting  values  assigned  to  shortness  and 
tallness,  would  have  a  sensible  effect  upon  the  result. 
I  am  therefore  content  to  ignore  it,  and  to  regard  the 
Statures  of  married  folk  just  as  if  their  choice  in  mar- 
riage had  been  wholly  independent  of  stature.  The 
importance  of  this  supposition  in  facilitating  calculation 
will  be  appreciated  as  we  proceed. 

Issue  of  Unlike  Parents. — AVe  will  next  discuss  the 
question  whether  the  Stature  of  the  issue  of  unlike 
parents  betrays  any  notable  evidence  of  their  unlikeness, 
or  whether  the  peculiarities  of  the  children  do  not  rather 
depend  on  the  average  of  two  values ;  one  the  Stature 
of  the  father,  and  the  other  the  transmuted  Stature 
of   the    mother ;    in    other    words,    on    the    Stature    of 


VII.]  DISCLTSICN  CF  THE  DATA  OF  STATURE.  89 

that  ideal  personage  to  wliom  we  have  akeady  been 
introduced  under  the  name  of  a  Mid- Parent.  Stature 
has  already  been  spoken  of  as  a  well-marked  instance 
of  the  heritages  that  blend  freely  in  the  course  of 
hereditary  transmission.  It  now  becomes  necessary  to 
substantiate  the  statement,  because  it  is  proposed  to 
trace  the  relationship  between  the  Mid-Parent  and  the 
Son.  It  would  not  be  possible  to  discuss  the  relationship 
between  either  parent  singly,  and  the  son,  in  a  trust- 
w^orthy  way,  without  the  help  of  a  much  larger  number 
of  observations  than  are  now  at  my  disposal.  They 
ought  to  be  numerous  enough  to  give  good  assurance  that 
the  casea  of  tall  and  short,  among  the  unknown  parents, 
shall  neutralise  one  another ;  otherwise  the  uncertainty 
of  the  stature  of  the  unknown  parent  would  make  the  re- 
sults uncertain  to  a  serious  degree.  I  am  heartily  glad 
that  I  shall  be  able  fully  to  justify  the  method  of  deal- 
ing with  Mid-Parentages  instead  of  with  single  Parents. 
The  evidence  is  as  follows  : — If  the  Stature  of  children 
depends  only  upon  the  average  Stature  of  their  two 
Parents,  that  of  the  mother  having  been  first  trans- 
muted, it  will  make  no  difi'erence  in  a  Fraternity  whether 
one  of  the  Parents  was  tall  and  the  other  short,  or 
whether  they  were  alike  in  Stature.  But  if  some  children 
resemble  one  Parent  in  Stature  and  others  resemble  the 
other,  the  Fraternity  will  be  more  diverse  when  their 
Parents  had  differed  in  Stature  than  when  they  were 
alike.  We  easily  acquaint  ourselves  with  the  facts  by 
separating  a  considerable  number  of  Fraternities  into 
two  contrasted  groups  :  (a)  those  who  are  the  progeny 


90  NATURAL  INHERITANCE.  ^cnAP. 

of  Like    Parents  ;    (b)   those   who   are   tlie  progeny  of 
Unlike    Parents.      Next  we  write  tlie    statures  of  the 
individuals    in    eacli    Fraternity    under    the    form    of 
M  +  (dzD)   (see  page  51),  where  M  is  the  mean  stature 
of  the  Fraternity,  and  D  is  the  deviation  of  any  one  of 
its  members  from  M.     Then  we  marshal  all  the  values 
of  D  that  belong  to  the  group  a,  into  one  Scheme  of 
de^dations,   and  all  those  that  belong  to  the  group  h 
into  another  Scheme,  and  we  find  the  Q  of  each.     If  it 
should  be  the  same,  then  there  is  no  greater  diversity 
in  the  a  Grroup  than  there  is  in  the  b  Group,  and  such 
proves  to  be  the  case.     I  applied  the  test  (see  Table  10) 
to  a  total  of  525  children,  and  found  that  they  were  no 
more  diverse   in  the  one   case   than   in   the    other.     I 
therefore  conclude  that  we  have  only  to  look  to  the 
Stature  of  the  Mid-Parent,  and  need  not  care  whether 
the  Parents  are  or  are  not  unlike  one  another. 

The  advantages  of  Stature  as  a  subject  from  which  the 
simple  laws  of  heredity  may  be  studied,  will  now  be 
well  appreciated.  It  is  nearly  constant  in  the  same 
adult,  it  is  frequently  measured  and  recorded  ;  its  dis- 
cussion need  not  be  entangled  with  considerations  of 
marriage  selection.  It  is  sufficient  to  consider  the  Stature 
of  the  Mid-Parent  and  not  those  of  the  two  Parents 
separately.  Its  variability  is  Normal,  so  that  much  use 
may  be  made  of  the  curious  properties  of  the  law  of 
Frequency  of  Error  in  cross-testing  the  several  con- 
clusions, and  I  may  add  that  in  all  cases  they  have 
borne  the  test  successfully. 


VII.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  91 

The  only  drawback  to  tlie  use  of  Stature  in  statistical 
inquiries,  is  its  small  variability,  one  balf  of  tbe  popula- 
tion differing  less  than  1'7  inch,  from  the  average  of  all 
of  tliem.     In  other  words,  its  Q  is  only  1'7  inch. 

Description  of  the  ToMes  of  Stature. — I  have  arranged 
and  discussed  my  materials  in  a  great  variety  of  ways,  to 
guard  against  rash  conclusions,  but  do  not  think  it 
necessary  to  trouble  the  reader  with  more  than  a  few 
Tables,  which  afford  sufficient  material  to  determine 
the  more  important  constants  in  the  formulae  that  will 
be  used. 

Table  11,  E.F.F.,  refers  to  the  relation  between  the 
Mid-Parent  and  his  (or  should  we  say  its  ?)  Sons  and 
Transmuted  Daughters,  and  it  records  the  Statures  of 
928  adult  offspring  of  205  Mid-Parents.  It  shows  the 
distribution  of  Stature  among  the  Sons  of  each  succes- 
sive group  of  Mid-Parents,  in  which  ^ the  latter  are  all 
~of  the  same  Stature,  reckoning  to  the  nearest  inch.  I 
have  calculated  the  M  of  each  line,  chiefly  by  drawing 
Schemes  from  the  entries  in  it.  Their  values  are  printed 
at  the  ends  of  the  lines  and  they  form  the  right-hand 
column  of  the  Table. 

Tables  12  and  13  refer  to  the  relation  between  Brothers. 
The  one  is  derived  frcm  the  E.F.F.  and  the  other  from 
the  Special  data.  They  both  deal  with  small  or  moder- 
ately sized  Fraternities,  excluding  the  larger  ones  for 
reasons  that  will  be  explained  directly,  but  the  E.F.F. 
Table  is  the  least  restricted  in  this  respect,  as  it  only 
excludes  families  of  6  brothers  and  upwards.     The  data 


92  NATURAL  INHERITANCE.  [chap. 

were  so  few  in  number  tliat  I  could  not  well  afford  to  lop 
off  more.  These  Tables  were  constructed  by  registering 
the  differences  between  each  possible  pair  of  brothers  in 
each  family :  thus  if  there  were  three  brothers,  A,  B, 
and  C,  in  a  particular  family,  I  entered  the  differences 
of  stature  between  A  and  B,  A  and  C,  and  B  and  C, 
four  brothers  gave  rise  to  6  entries,  and  five  brothers  to 
10  entries.  The  larger  Fraternities  were  omitted,  as  the 
very  large  number  of  different  pairs  in  them  would 
have  overwhelmed  the  influence  of  the  smaller  Frater- 
nities. Large  Fraternities  are  separately  dealt  with  in 
Table  14. 

We  can  derive  some  of  the  constants  by  more  than 
one  method ;  and  it  is  gratifying  to  find  how  well  the 
results  of  different  methods  confirm  one  another. 

Mid-Stature  of  the  Population. — The  Median,  Mid- 
Stature,  or  M  of  'the  general  Population  is  a  value  of 
primary  importance  in  this  inquiry.  Its  value  will  be 
always  designated  by  the  symbol  P,  and  it  may  be 
deduced  from  the  bottom  lines  of  any  one  of  the  three 
Tables.  I  obtain  from  them  respectively  the  values 
6 8 '2,  68 '5,  68 '4,  but  the  middle  of  these,  which  is 
printed  in  italics,  is  a  smoothed  result.  It  is  one  of  the 
only  two  smoothed  values  in  the  whole  of  my  work,  and 
was  justifiably  corrected,  because  the  observed  values 
that  happen  to  lie  nearest  to  the  Grade  of  50°  ran  out  of 
harmony  with  the  rest  of  the  curve.  It  is  therefore 
reasonable  to  consider  its  discrepancy  as  fortuitous, 
althouQ-h   it  amounts   to    more    than    0'15   inch.      The 


VII.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  93 

series  in  question  refers  to  E.F.F.  brothers,  wlio,  owing 
to  the  principle  on  whicli  the  Table  is  constructed,  are 
only  a  comparatively  small  sample  taken  out  of  the 
E.F.F.  Population,  and  on  a  principle  that  gave  greater 
weight  to  a  few  large  families  than  to  all  the  rest. 
Therefore  it  could  not  be  expected  to  give  rise  to  so 
regular  a  Scheme  for  the  general  E.F.F.  Population 
as  Table  11,  which  was  fairly  based  upon  the  whole 
of  it.  Less  accuracy  was  undoubtedly  to  have  been 
expected  in  this  group  than  in  either  of  the  others. 

Variahility  of  the  Population. — The  value  of  Q  in 
the  Statures  of  the  general  Population  is  to  be  deduced 
from  the  bottom  lines  of  any  one  of  the  Tables  11,  12, 
and  13.  The  three  values  of  it  that  I  so  obtain,  are 
1'65,  1*7,  and  1'7  inch.  I  should  mention  that  the 
method  of  the  treatment  originally  adopted,  happened 
also  to  make  the  first  of  these  values  1  '7  inch,  so  I  have 
no  hesitation  in  accepting  1*7  as  the  value  for  all  my 
ciaLa. 

Variability  of  Mid-Parents. — The  value  of  Q  in  a 
Scheme  drawn  from  the  Statures  of  the  E.F.F.  Mid- 
Parents  according  to  the  data  in  Table  11,  is  1'19 
inches.  Now  it  has  already  been  shown  that  if  marriage 
selection  is  independent  of  stature,  the  value  of  Q  in  the 
Scheme  of  Mid-parental  Statures  would  be  ec[ual  to  its 
value  in  that  of  the  general  Population  (which  we  have 
just  seen  to  be  1*7  inch),  divided  by  the  square  root  of 
2  ;  that  is  by  1'45.     This  calculation  makes  it  to  be 


94  NATURAL  INHERITANCE.  .  [chap. 

1*21   iiicli,  which  agrees  excellently  with  the  observed 
value/ 

Variahilky  in  Co- Fraternities. — As  all  the  Adult 
Sons  and  Transmuted  Daughters  of  the  same  Mid- 
Parent,  form  what  is  called  a  Fraternity,  so  all  the  Adult 
Sons  and  Transmuted  Daughters  of  a  group  of  Mid- 
Parents  who  have  the  same  Stature  (reckoned  to  the 
nearest  inch)  will  be  termed  a  Co-Fraternity.  Each 
line  in  Table  11  refers  to  a  separate  Co-Fraternity  and 
expresses  the  distribution  of  Stature  among  them. 
There  are  three  reasons  why  Co-Fraternals  should  be 
more  diverse  among  themselves  than  brothers.  First, 
because  their  Mid-Parents  are  not  of  identical  height, 
but  may  differ  even  as  much  as  one  inch.  Secondly, 
because  their  grandparents,  great-grandparents,  and  so 
on  indefinitely  backwards,  may  have  difi'ered  widely. 
Thirdly,  because  the  nurture  or  rearing  of  Co-Fraternals 
is  more  various  than  that  of  Fraternals.  The  brothers 
in  a  Fraternity  of  townsfolk  do  not  seem  to  difi'er  more 
among  themselves  than  those  in  a  Fraternity  of  country- 
folk, but  a  mixture  of  Fraternities  derived  indiscrimi- 
nately from  the  two  sources,  must  show  greater  diversity 
than  either  of  them  taken  by  themselves.  The  large 
difi'erences  between  town  and  country-folk,  and  those 
between  persons  of  difi'erent  social  classes,  are  con- 
spicuous in  the   data  contained  in  the  Report  of  the 

'^  In  all  my  values  referring  to  liuman  stature,  tlie  second  decimal  is 
rudely  approximate.  I  am  obliged  to  use  it,  because  if  I  worked  only  to 
tentlis  of  an  incli,  sensible  errors  might  creep  in  entirely  owing  to  aritli- 
metical  operations. 


vii.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  95 

Anthropological   Committee  to   the  British  Association 
in   1880,  and  published  in  its  Journal. 

I  concluded  after  carefully  studying  the  chart  upon 
which  each  of  the  individual  observations  from  which 
Table  11  was  constructed,  had  been  entered  separately 
in  their  appropriate  places,  and  not  clubbed  into  groups 
as  in  the  Tables,  that  the  value  of  Q  in  each  Co- 
Fraternal  group  was  roughly  the  same,  whatever  their 
Mid-Parental  value  might  have  been.  It  was  not  cjuite 
the  same,  being  a  trifle  larger  when  the  Mid-Parents 
were  tall  than  when  they  were  short.  This  justifies 
what  will  be  said  in  Appendix  E  about  the  G-eometric 
Mean ;  it  also  justifies  neglect  in  the  present  inquiry  of 
the  method  founded  upon  it,  because  the  improvement 
in  the  results  to  which  it  might  lead,  would  be  insignifi- 
cant, while  its  use  would  have  added  to  the  difiiculty 
of  explanation,  and  introduced  extra  trouble  throuo-h- 
out,  to  the  reader  more  than  to  myself.  The  value  that 
I  adopt  for  Q  in  every  Co-Fraternal  group,  is  1*5  inch. 

Regression. — a.  Filial :  However  paradoxical  it  may 
appear  at  first  sight,  it  is  theoretically  a  necessary  fact, 
and  one  that  is  clearly  confirmed  by  observation,  that 
the  Stature  of  the  adult  ofi*spring  must  on  the  whole, 
be  more  mediocre  than  the  stature  of  their  Parents  ; 
that  is  to  say,  more  near  to  the  IVI  of  the  general 
Population.  Table  11  enables  us  to  compare  the 
values  of  the  IVI  in  difi'erent  Co-Fraternal  groups 
with  the  Statures  of  their  respective  Mid-Parents. 
Fig.  10  is  a  graphical  representation  of  the  meaning  of 


96 


NATURAL  INHERITANCE. 


[chap. 


the  Table  so  far  as  it  now  concerns  ns.  The  horizontal 
dotted  lines  and  the  graduations  at  their  sides,  cor- 
respond to  the  similarly  placed  lines  of  figures  and 
graduations  in  Table  11.  The  dot  on  each  line  shows 
the  point  where  its  IVI  falls.  The  value  of  its  M  is  to 
be  read  on  the  graduations  along  the  top,  and  is  the 
same  as  that  which  is  given  in  the  last  column  of 
Table   11.      It  will  be   perceived  that  the  line  drawn 

FIG.EO. 


through  the  centres  of  the  dots,  admits  of  being  inter- 
preted by  the  straight  line  C  D,  with  but  a  small 
amount  of  give  and  take  ;  and  the  fairness  of  this 
interpretation  is  confirmed  by  a  study  of  the  MS.  chart 
above  mentioned,  in  which  the  individual  observations 
were  plotted  in  their  right  places. 

Now  if  we  draw  a  line  A  B  through  every  point  where 
the  graduations  along  the  top  of  Fig.  10,  are  the  same 
as  those  along  the  sides,  the  line  will  be  straight  and. 
will    run    diagonally.      It    represents    what    the    Mid- 


VII.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  97 

Statures  of  the  Sons  would  be,  if  tliey  were  on  tlie 
average  identical  with  those  of  their  Mid-Parents. 
Most  obviously  A  B  does  not  agree  with  C  D  ;  therefore 
Sons  do  not,  on  the  average,  resemble  their  Mid- 
Parents.  On  examining  these  lines  more  closely,  it 
will  be  observed  that  A  B  cuts  C  D  at  a  point  M  that 
fairly  corresponds  to  the  value  of  685-  inches,  whether 
its  value  be  read  on  the  scale  at  the  top  or  on  that  at 
the  side.  This  is  the  value  of  P,  the  Mid-Stature  of 
the  population.  Therefore  it  is  only  when  the  Parents 
are  mediocre,  that  their  Sons  on  the  average  resemble 
them. 

Next  draw  a  vertical  line,  E  M  F,  through  M,  and 
let  EGA  be  any  horizontal  line  cutting  ME  at  E,  MC 
at  E,  and  MA  at  A.  Then  it  is  obvious  that  the  ratio  of 
EA  to  EC  is  constant,  whatever  may  be  the  position  of 
E  C  A.  This  is  true  whether  E  C  A  be  drawn  above  or 
like  F  D  B,  below  M.  In  other  words,  the  proportion 
between  the  Mid-Filial  and  the  Mid-Parental  deviation 
is  constant,  whatever  the  Mid-Parental  stature  may  be. 
I  reckon  this  ratio  to  be  as  2  to  3  :  that  is  to  say,  the 
Filial  deviation  from  P  is  on  the  average  only  two- 
thirds  as  wide  as  the  Mid-Parental  Deviation.  I  call 
this  ratio  of  2  to  3  the  ratio  of  "  Filial  Eegression."  It 
is  the  proportion  in  which  the  Son  is,  on  the  average, 
less  exceptional  than  his  Mid-Parent. 

My  first  estimate  of  the  average  proportion  between 
the  Mid-Filial  and  the  Mid-Parental  deviations,  was 
made  from  a  study  of  the  MS.  chart,  and  I  then 
reckoned  it  as  3  to  5.     The  value   given   above   was 

H 


98  NATURAL  INHERITANCE.  [chap. 

afterwards  substituted,  because  the  data  seemed  to 
admit  of  that  interpretation  also,  in  which  case  the 
fraction  of  two-thirds  was  preferable  as  being  the  more 
simple  expression.  I  am  now  inclined  to  think  the 
latter  may  be  a  trifle  too  small,  but  it  is  not  worth 
while  to  make  alterations  until  a  new,  larger,  and  more 
accurate  series  of  observations  can  be  discussed,  and  the 
whole  work  revised.  The  present  doubt  only  ranges 
between  nine-fifteenths  in  the  first  case  and  ten- 
fifteenths  in  the  second. 

This  value  of  two-thirds  will  therefore  be  accepted  as 
the  amount  of  Eegression,  on  the  average  of  many 
cases,  from  the  Mid-Parental  to  the  Mid-Filial  stature, 
whatever  the  Mid-Parental  stature  may  be. 

As  the  two  Parents  contribute  equally,  the  contribu- 
tion of  either  of  them  can  be  only  one  half  of  that 
of  the  two  jointly  ;  in  other  words,  only  one  half  of  that 
of  the  Mid-Parent.  Therefore  the  average  Eegression 
from  the  Parental  to  the  Mid-Filial  Stature  must  be  the 
one  half  of  two-thirds,  or  one-third.  I  am  unable  to 
test  this  conclusion  in  a  satisfactory  manner  by  direct 
observation.  The  data  are  barely  numerous  enough  for 
dealing  even  with  questions  referring  to  Mid- Parentages  ; 
they  are  quite  insufficient  to  deal  with  those  that  involve 
the  additional  large  uncertainty  introduced  owing  to  an 
ignorance  of  the  Stature  of  one  of  the  parents.  I  have 
entered  the  Uni-Parental  and  the  Filial  data  on  a 
MS.  chart,  each  in  its  appropriate  place,  but  they  are 
too  scattered  and  irregular  to  make   it  useful   to  give 


VII.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  99 

the  results  in  detail.  They  seem  to  show  a  Eegression 
of  about  two-fifths,  which  differs  from  that  of  one-third 
in  the  ratio  of  6  to  5.  This  direct  observation  is  so 
inferior  in  value  to  the  inferred  result,  that  I  disregard 
it,  and  am  satisfied  to  adopt  the  value  given  by  the 
latter,  that  is  to  say,  of  one-third,  to  express  the 
averag^e  Recession  from  either  of  the  Parents  to  the 
Son. 

h.  Mid-Parental :  The  converse  relation  to  that  which 
we  have  just  discussed,  namely  the  relation  between 
the  unknown  stature  of  the  Mid-Parent  and  the  known 
Stature  of  the  Son,  is  expressed  by  a  fraction  that  is 
very  far  from  being  the  converse  of  two-thirds.  Though 
the  Son  deviates  on  the  average  from  P  only  f  as 
widely  as  his  Mid-parent,  it  does  not  in  the  least  follow 
that  the  Mid-parent  should  deviate  on  the  average  from 
P,  1^  or  1-J-,  as  widely  as  the  Son.  The  Mid-Parent  is 
not  likely  to  be  more  exceptional  than  the  son,  but 
quite  the  contrary.  The  number  of  individuals  who 
are  nearly  mediocre  is  so  preponderant,  that  an  ex- 
ceptional man  is  more  frequently  found  to  be  the 
exceptional  son  of  mediocre  parents  than  the  average 
son  of  very  exceptional  parents.  This  is  clearly  shown 
by  Table  1 1 ,  where  the  very  same  observations  which  give 
the  average  value  of  Filial  Regression  when  it  is  read 
in  one  way,  gives  that  of  the  Mid-Parental  Regression 
when  it  is  read  in  another  way,  namely  down  the  vertical 
columns,  instead  of  along  the  horizontal  lines.  It  then 
shows  that  the  Mid-Parent  of  a  man  deviates  on  the 

H  2 


100  NATURAL  INHERITANCE.  [chap. 

average  from  P,  only  one-third  as  much,  as  tlie  man 
himself.  This  value  of  -^  is  four  and  a  half  times 
smaller  than  the  numerical  converse  of  f ,  since  A^,  or 
f,  being  multiplied  into  ^,  is  equal  to  f . 

c.  Parental :  As  a  Mid-Parental  deviation  is  equal 
to  one-half  of  the  two  Parental  deviations,  it  follows 
that  the  Mid-Parental  Eegression  must  be  ecjual  to 
one-half  of  the  sum  of  the  two  Parental  Regressions. 
As  the  latter  are  equal  to  one  another  it  follows  that 
all  three  must  have  the  same  value.  In  other  words, 
the  average  Mid-Parental  Regression  being  ^,  the 
average  Parental  Regression  must    be  -J-  also. 

As  there  was  much  appearance  of  paradox  in  the 
above  strongly  contrasted  results,  I  looked  carefully 
into  the  run  of  the  figures  in  Table  11.  They  were 
deduced,  as  already  said,  from  a  MS.  chart  on  which 
the  stature  of  every  Son  and  the  transmuted  Stature  of 
every  Daughter  is  entered  opposite  to  that  of  the  Mid- 
Parent,  the  transmuted  Statures  being  reckoned  to  the 
nearest  tenth  of  an  inch,  and  the  position  of  the  other 
entries  being  in  every  respect  exactly  as  they  were 
recorded.  Then  the  number  of  entries  in  each  square 
inch  were  counted,  and  copied  in  the  form  in  which 
they  ajDpear  in  the  Table.  I  found  it  hard  at  first 
to  catch  the  full  significance  of  the  entries,  though  1 
soon  discovered  curious  and  apparently  very  interesting 
relations  between  them.  These  came  out  distinctly 
after  I  had  ''  smoothed "  the  entries  by  writing  at 
each  intersection  between  a  horizontal  line  and  a  ver- 


VII.] 


DISCUSSION  OF  THE  DATA  OF  STATURE. 


101 


tical  one,  tlie  sum  of  the  entries  in  the  four  adjacent 
squares.  I  then  noticed  (see  Fig.  11)  that  lines  drawn 
through  entries  of  the  same  value  formed  a  series  of 
concentric  and  similar  ellipses.  Their  common  centre 
lay  at  the  intersection  of  those  vertical  and  horizontal 
lines  which  correspond  to  the  value  of  68 J  inches,  as 
read  on  both  the  top  and  on  the  side  scales.  Their 
axes  were  similarly  inclined.  The  points  where  each 
successive  ellipse  was  touched  by  a  horizontal  tangent, 
lay  in  a  straight  line  that  was  inclined  to  the  vertical  in 


FIG. II. 


A 

Y 

\ 

'N 

/ 

'-"/P   J^\ 

m: 

k 

^ 

^ 

the  ratio  of  f,  and  those  where  the  ellipses  were  touched 
by  a  vertical  tangent,  lay  in  a  straight  line  inclined  to 
the  horizontal  in  the  ratio  of  \.  It  will  be  obvious 
on  studying  Fig.  11  that  the  point  where  each  suc- 
cessive horizontal  line  touches  an  ellipse  is  the  point 
at  which  the  greatest  value  in  the  line  will  be  found. 
The  same  is  true  in  respect  to  the  successive  vertical  lines. 
Therefore  these  ratios  confirm  the  values  of  the  Eatios 
of  Eegression,  already  obtained  by  a  different  method, 
namely  those  of  f  from   Mid-Parent   to    Son,    and   of 


102  NATURAL  INHERITANCE.  [chip. 

^-  from  Son  to  Mid-Parent.  These  and  other  re- 
lations were  evidently  a  subject  for  matliematical 
analysis  and  verification.  It  seemed  clear  to  me  that 
they  all  depended  on  three  elementary  measures,  sup- 
posing the  law  of  Frequency  of  Error  to  be  applicable 
throughout ;  namely  (l)  the  value  of  Q  in  the  General 
Population,  which  was  found  to  be  17  inch;  (2)  the 
value  of  Q  in  any  Co-Fraternity,  which  was  found  to  be 
1*5  inch;  (3)  the  Average  Eegression  of  the  Stature  of 
the  Son  from  that  of  the  Mid-Parent,  which  was  found 
to  be  f .  I  wrote  down  these  values,  and  phrasing  the 
problem  in  abstract  terms,  disentangled  from  all  refer- 
ence to  heredity,  submitted  it  to  Mr.  J.  T>,  Hamilton 
Dickson,  Tutor  of  St.  Peter's  College,  Cambridge  (see 
Appendix  B).  I  asked  him  kindly  to  investigate  for 
me  the  Surface  of  Frequency  of  Error  that  would  result 
from  these  three  data,  and  the  various  shapes  and  other 
particulars  of  its  sections  that  were  made  by  horizontal 
planes,  inasmuch  as  they  ought  to  form  the  ellipses  of 
which  I  spoke. 

The  problem  may  not  be  difficult  to  an  accomplished 
mathematician,  but  I  certainly  never  felt  such  a  glow 
of  loyalty  and  respect  towards  the  sovereignty  and  wide 
sway  of  mathematical  analysis  as  when  his  answer  arrived, 
confirming,  by  purely  mathematical  reasoning,  my  vari- 
ous and  laborious  statistical  conclusions  with  far  more 
minuteness  than  I  had  dared  to  hope,  because  the  data 
ran  somewhat  roughly,  and  I  had  to  smooth  them  with 
tender  caution.  His  calculation  corrected  my  observed 
value  of  Mid- Parental  Eegression  from  ^  to  yf  tt  '>  ^^^^ 


VII.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  103 

relation  between  the  major  and  minor  axis  of  the 
ellipses  was  changed  3  per  cent.  ;  and  their  inclination 
to  one  another  was  changed  less  than  2°.^ 

It  is  obvious  from  this  close  accord  of  calculation 
with  observation,  that  the  law  of  Error  holds  through- 
out with  sufficient  precision  to  be  of  real  service,  and 
that  the  various  results  of  my  statistics  are  not 
casual  and  disconnected  determinations,  but  strictly 
interdependent. 

I  trust  it  will  have  become  clear  even  to  the  most 
non-mathematical  reader,  that  the  law  of  Eegression 
in  Stature  refers  primarily  to  Deviations,  that  is,  to 
measurements  made  from  the  level  of  -mediocrity  to  the 

1  The  following  is  a  more  detailed  comparison  between  tlie  calculated 
and  tlie  observed  results.     The  latter  are  enclosed  in  brackets.    The  letters 
refer  to  Fig.  11  : — 
Given — 

The  "Probable  Error"  of  each   system  of  Mid- Parentages  =  1-22 
inch.    (This  was  an  earlier  determination  of  its  value  ;  as  already  said, 
the  second  decimal  is  to  be  considered  only  as  approximate.) 
Eatio  of  mean  filial  regression  =  f . 
"  Prob.  Error"  of  each  Co-Fraternity  =  1*50  inch. 


Sections  of  surface  of  frequency  parallel  to  XY  are  true  ellipses. 

(Obs. — Apparently  true  ellipses.) 
MX  :  YO  =  6  :  17*5,  or  nearly  1:3. 

(Obs.— 1  :  3.) 
Major  axes  to  minor  axes  =  ^  1  '.  ^^2  =  10:  5*35. 

(Obs.— 10  :  5-1.) 
Inclination  of  major  axes  to  OX  =  26°  36'. 

(Obs.  25°. ) 
Section  of  surface  parallel  to  XZ  is  a  true  Curve  of  Frequency. 

(Obs. — Apparently  so.) 
"  Prob.  Error  ",  the  Q  of  that  curve,  =  1.07  inch. 

(Obs.— 1 '00,  or  a  little  more.) 


104  NATURAL  INHERITANCE.  [chap. 

crown  of  the  liead,  upwards  or  downwards  as  the  case 
may  be,  and  not  from  the  ground  to  the  crown  of  the 
head.  (In  the  po23ulation  with  which  I  am  now  dealing, 
the  level  of  mediocrity  is  68 J  inches  (without  shoes).) 
The  law  of  Regression  in  respect  to  Stature  may  be 
phrased  as  follows ;  namely,  that  the  Deviation  of  the 
Sons  from  P  are,  on  the  average,  equal  to  one-third  of 
the  deviation  of  the  Parent  from  P,  and  in  the  same 
direction.  Or  more  briefly  still : — If  P  -1-  (zt  D)  be  the 
Stature  of  the  Parent,  the  Stature  of  the  offspring  will 
on  the  average  be  P  +  (zb  |-  D). 

If  this  remarkable  law  of  Regression  had  been  based 
only  on  those  experiments  with  seeds,  in  which  I  first 
observed  it,  it  might  weU  be  distrusted  until  otherwise 
confirmed.  If  it  had  been  corroborated  by  a  compara- 
tively small  number  of  observations  on  human  stature, 
some  hesitation  might  be  expected  before  its  truth  could 
be  recognised  in  opposition  to  the  current  belief  that  the 
child  tends  to  resemble  its  parents.  But  more  can  be 
urged  than  this.  It  is  easily  to  be  shown  that  we  ought 
to  expect  Filial  Regression,  and  that  it  ought  to  amount 
to  some  constant  fractional  part  of  the  value  of  the  Mid- 
Parental  deviation.  All  of  this  will  be  made  clear  in  a 
subsequent  section,  when  we  shall  discuss  the  cause  of 
the  curious  statistical  constancy  in  successive  generations 
of  a  large  population.  In  the  meantime,  two  different 
reasons  may  be  given  for  the  occurrence  of  Regression  ; 
the  one  is  connected  with  our  notions  of  stability  of 
type,  and  of  which  no  more  need  now  be  .  said ;  the 
other  is  as  follows  : — The  child  inherits  partly  from  his 


VII.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  105 

parents,  partly  from  liis  ancestry.  In  every  population 
tliat  intermarries  freely,  wlien  the  genealogy  of  any  man 
is  traced  far  backwards,  liis  ancestry  will  be  found  to 
consist  of  such  varied  elements  that  they  are  indistin- 
guishable from  a  sample  taken  at  haphazard  from  the 
general  Population.  The  Mid- Stature  IVI  of  the  remote 
ancestry  of  such  a  man  will  become  identical  with  P ; 
in  other  words,  it  will  be  mediocre.  To  put  the  same 
conclusion  into  another  form,  the  most  probable  value 
of  the  Deviation  from  P,  of  his  Mid- Ancestors  in  any 
remote  generation,  is  zero. 

For  the  moment  let  us  confine  our  attention  to  some 
one  generation  in  the  remote  ancestry  on  the  one  hand, 
and  to  the  Mid-Parent  on  the  other,  and  ignore  all 
other  generations.  The  combination  of  the  zero  Devia- 
tion of  the  one  with  the  observed  Deviation  of  the  other 
is  the  combination  of  nothing  with  something.  Its 
efi'ect  resembles  that  of  pouring  a  measure  of  water 
into  a  vessel  of  wine.  The  wine  is  diluted  to  a  con- 
stant fraction  of  its  alcoholic  strength,  whatever  that 
strength  may  have  been. 

Similarly  with  regard  to  every  other  generation. 
The  Mid-Deviation  in  any  near  generation  of  the 
ancestors  will  have  a  value  intermediate  between  that 
of  the  zero  Deviation  of  the  remote  ancestry,  and  of  the 
observed  Deviation  of  the  Mid-Parent.  Its  combination 
with  the  Mid-Parental  Deviation  will  be  as  if  a  mixture 
of  wine  and  water  in  some  definite  proportion,  and  not 
pure  water,  had  been  poured  into  the  wine.  The  process 
throughout  is  one  of  proportionate  dilutions,  and  the 


106  NATURAL  INHERITANCE.  [chap. 

joint  effect  of   all  of  tliem  is  to  weaken  the   original 
alcoholic  strength  in  a  constant  ratio. 

The  law  of  Eegression  tells  heavily  against  the  full 
hereditary  transmission  of  any  gift.  Only  a  few  out  of 
many  children  would  be  likely  to  differ  from  mediocrity 
so  widely  as  their  Mid-Parent,  and  still  fewer  would 
differ  as  widely  as  the  more  exceptional  of  the  two 
Parents.  The  more  bountifully  the  Parent  is  gifted 
by  nature,  the  more  rare  will  be  his  good  fortune 
if  he  begets  a  son  who  is  as  richly  endowed  as  himself, 
and  still  more  so  if  he  has  a  son  who  is  endowed  yet 
more  largely.  But  the  law  is  even-handed ;  it  levies  an 
equal  succession-tax  on  the  transmission  of  badness  as  of 
goodness.  If  it  discourages  the  extravagant  hopes  of  a 
gifted  parent  that  his  children  will  inherit  all  his  powers  ; 
it  no  less  discountenances  extravagant  fears  that  they 
will  inherit  all  his  weakness  and  disease. 

It  must  be  clearly  understood  that  there  is  nothing  in 
these  statements  to  invalidate  the  general  doctrine  that 
the  children  of  a  gifted  pair  are  much  more  likely  to  be 
gifted  than  the  children  of  a  mediocre  pair.  They 
merely  express  the  fact  that  the  ablest  of  all  the 
children  of  a  few  gifted  pairs  is  not  likely  to  be  as 
gifted  as  the  ablest  of  all  the  children  of  a  very  great 
many  mediocre  pairs. 

The  constancy  of  the  ratio  of  Eegression,  whatever 
may  be  the  amount  of  the  Mid-Parental  Deviation,  is 
now  seen  to  be  a  reasonable  law  which  might  have  been 
foreseen.     It  is  so  simple  in  its  relations  that  I  have 


VII.] 


DISCUSSION  OF  THE  DATA  OF  STATURE. 


107 


FIG  .12. 


contrived  more  than  one  form  of  apparatus  by  which 
the  probable  stature  of  the  children  of  known  parents 
can  be  mechanically  reckoned.  Fig.  12  is  a  representation 
of  one  of  them,  that  is  worked  with  pulleys  and  weights. 
A,  B,  and  C  are  three  thin  wheels  with  grooves  round 
their  edges.  They  are  screwed 
together  so  as  to  form  a  single 
piece  that  turns  easily  on  its 
axis.  The  weights  M  and  F  are 
attached  to  either  end  of  a  thread 
that  passes  over  the  movable 
pulley  D.  The  pulley  itself  hangs 
from  a  thread  which  is  wrapped 
two  or  three  times  round  the 
groove  of  B  and  is  then  secured 
to  the  wheel.  The  weight  SD 
hangs  from  a  thread  that  is 
wrapped  two  or  three  times  round 
the  groove  of  A,  and  is  then 
secured  to  the  wheel.  The  dia- 
meter of  A  is  to  that  of  B  as  2 
to  3.  Lastly,  a  thread  is  wrapped 
in  the  opposite  direction  round 
the  wheel  C,  which  may  have 
any  convenient  diameter,  and  is 
attached  to  a  counterpoise.  M  refers  to  the  male  statures, 
F  to  the  female  ones,  S  to  the  Sons,  D  to  the  Daughters. 
The  scale  of  Female  Statures  differs  from  that  of  the 
Males,  each  Female  height  being  laid  down  in  the 
position  which  would  be  occupied  by  its  male  equivalent. 


108  NATURAL  INHERITANCE.  [chap. 

Tims  56  is  written  in  the  position  of  60*48  inches,  wliich 
is  equal  to  56x1*08.  Similarly,  60  is  written  in  the 
position  of  64*80,  which  is  equal  to  60  x  1*08. 

It  is  obvious  that  raising  M  will  cause  F  to  fall,  and 
vice  versa,  without  affecting  the  wheel  AB,  and  there- 
fore without  affecting  SD ;  that  is  to  say,  the  Parental 
Differences  may  be  varied  indefinitely  without  affecting 
the  Stature  of  the  children,  so  long  as  the  Mid-Parental 
Stature  is  unchanged.  But  if  the  Mid-Parental  Stature 
is  changed  to  any  specified  amount,  then  that  of  SD 
will  be  changed  to  f  of  that  amount. 

The  weights  M  and  F  have  to  be  set  opposite  to  the 
heights  of  the  mother  and  father  on  their  respective 
scales ;  then  the  weight  SD  will  show  the  most  probable 
heights  of  a  Son  and  of  a  Daughter  on  the  corresponding 
scales.  In  every  one  of  these  cases,  it  is  the  fiducial 
mark  in  the  middle  of  each  weight  by  which  the  reading 
is  to  be  made.  But,  in  addition  to  this,  the  length  of 
the  weight  SD  is  so  arranged  that  it  is  an  equal  chance 
(an  even  bet)  that  the  height  of  each  Son  or  each 
Daughter  will  lie  within  the  range  defined  by  the  upper 
and  lower  edge  of  the  weight,  on  their  respective  scales. 
The  length  of  SD  is  3  inches,  which  is  twice  the  Q  of 
the  Co-Fraternity ;  that  is,  2  x  1*50  inch. 

d.  Fraternal :  In  seeking  for  the  value  of  Fraternal 
Regression,  it  is  better  to  confine  ourselves  to  the 
Special  data  given  in  Table  13,  as  they  are  much 
more  trustworthy  than  the  R.F.F.  data  in  Table  12. 
By  treating  them  in  the  way  shown  in  Fig.  13,  which 
is  constructed  on  the  same  principle  as  Fig.  10,  page  96, 


VII.] 


DISCUSSION  OF  THE  DxiTA  OF  STATURE. 


109 


2.  . 
3  ' 


I  obtained  the  value  for  Fraternal  Eegression  of 
that  is  to  say,  the  unknown  brother  of  a  known  man  is 
probably  only  two-thirds  as  exceptional  in  Stature  as 
he  is.  This  is  the  same  value  as  that  obtained  for  the 
Regression  from  Mid-Parent  to  Son.  However  para- 
doxical the  fact  may  seem  at  first,  of  there  being  such 
a  thing  as  Fraternal  Regression,  a  little  reflection  will 
show  its  reasonableness,  which  will  become  much  clearer 
later  on.     In  the  meantime,  we  may  recollect  that  the 


F\Cr  A3. 


FRATERNAL            REGRESSION 

R.F.F. 

64          6S          6S           70          72 

SPECfALS 

64          €6         68          70         73 

'       I      '       J             .1.1 

7B 

70 
6S 
66 
64 

- 

e  /            / 
1*    / 

72, 
70 

68 

€6 

6^ 

*/     / 

/          /' 

1         1         I         1 

1       1      1      1  \ 

1 I 1 I— 

unknown  brother  has  two  different  tendencies,  the  one 
to  resemble  the  known  man,  and  the  other  to  resemble 
his  race.  The  one  tendency  is  to  deviate  from  P  as 
much  as  his  brother,  and  the  other  tendency  is  not 
to  deviate  at  all.     The  result  is  a  compromise. 

As  the  average  Regression  from  either  Parent  to  the 
Son  is  twice  as  great  as  that  from  a  man  to  his  Brother, 
a  man  is,  generally  speaking,  only  half  as  nearly  related 


110  NATURAL  INHERITANCE.  [cuap. 

to  either  of  his  Parents  as  he  is  to  his  Brother.  In 
other  words,  the  Parental  kinship  is  only  half  as  close 
as  the  Fraternal. 

We  have  now  seen  that  there  is  Eegression  from  the 
Parent  to  his  Son,  from  the  Son  to  his  Parent,  and  from 
the  Brother  to  his  Brother.  As  these  are  the  only  three 
possible  lines  of  kinship,  namely,  descending,  ascending, 
and  collateral,  it  must  be  a  universal  rule  that  the  un- 
known Kinsman,  in  any  degree,  of  a  known  Man,  is  on 
the  average  more  mediocre  than  he.  Let  PitD  be  the 
stature  of  the  known  man,  and  PdzP)'  the  stature  of  his 
as  yet  unknown  kinsman,  then  it  is  safe  to  wager,  in 
the  absence  of  all  other  knowledge,  that  D^  is  less 
than  D. 

Squadron  of  Statures.— It  is  an  axiom  of  statistics, 
as  I  need  hardly  repeat,  that  every  large  sample  taken 
at  random  out  of  any  still  larger  group,  may  be  con- 
sidered as  identical  in  its  composition,  in  such  inquiries 
as  these  in  which  we  are  now  engaged,  where  minute 
accuracy  is  not  desired  and  where  highly  exceptional 
cases  are  not  regarded.  Suppose  our  larger  group  to 
consist  of  a  million,  that  is  of  1000  x  1000  statures,  and 
that  we  had  divided  it  at  random  into  1000  samples 
each  containing  1000  statures,  and  made  Schemes  of 
each  of  them.  The  1000  Schemes  would  be  practically 
identical,  and  we  mioiit  marshal  them  one  behind  the 
other  in  successive  ranks,  and  thereby  form  a  "  Squad- 
ron," numbering  1000  statures  each  way,  and  standing 


VII.] 


DISCUSSION  OF  THE  DATA  OF  STATURE. 


Ill 


upon  a  square  base.  Our  Squadron  may  be  divided 
either  into  1000  ranks  or  into  1000  files.  The  ranks 
will  form  a  series  of  1000  identical  Schemes,  the  files 
will  form  a  series  of  1000  rectangles,  that  are  of  the 
same  breadth,  but  of  dissimilar  heights.  (See  Fig.  14.) 
It  is  easy  by  this  illustration  to  give  a  general  idea, 
to  be  developed  as  we  proceed,  of  the  way  in  which  any 
large  sample,  A,  of  a  Population  gives  rise  to  a  group 
of  Kinsmen,  Z,  so  distant  as  to  retain  no  family  likeness 


FIG. 14 


to  A,  but  to  be  statistically  undistinguishable  from  the 
Population  generally,  as  regards  the  distribution  of  their 
statures.  In  this  case  the  samples  A  and  Z  would  form 
similar  Schemes.  I  must  suppose  provisionally,  for  the 
purpose  of  easily  arriving  at  an  approximate  theory, 
that  tall,  short,  and  mediocre  Parents  contribute  equally 
to  the  next  generation  though  this  may  not  strictly 
be  the  case.^ 

1  Oddly  enough,  the  shortest  couple  on  my  list  have  the  largest  family, 
namely,  sixteen  children,  of  whom  fourteen  were  measured. 


112  NATUIIAL  INHERITANCE.  [chap. 

Tlirow  A  into  the  form  of  a  Squadron  and  not  of  a 
Scheme,  and  let  us  begin  by  confining  our  attention 
to  the  men  who  form  any  two  of  the  rectangular  files 
of  A,  that  we  please  to  select.  Then  let  us  trace 
their  connections  with  their  respective  Kinsmen  in  Z. 
As  the  number  of  the  Z  Kinsmen  to  each  of  the  A  files 
is  considered  to  be  the  same,  and  as  their  respective 
Stature-Schemes  are  supposed  to  be  identical  with  that 
of  the  general  Population,  it  follows  that  the  two  Schemes 
in  Z  derived  from  the  two  difi'erent  rectangular  files  in 
A,  will  be  identical  with  one  another.  Every  other 
rectangular  file  in  A  will  be  similarly  represented  by 
another  identical  Scheme  in  Z.  Therefore  the  1,000 
difi'erent  rectangular  files  in  A  will  produce  1,000  iden- 
tical Schemes  in  Z,  arranged  as  in  Fig.  14. 

Though  all  the  Schemes  in  Z,  contain  the  same 
number  of  measures,  each  will  contain  many  more 
measures  than  were  contained  in  the  files  of  A,  because 
the  same  kinsmen  would  usually  be  counted  many 
times  over.  Thus  a  man  may  be  counted  as  uncle  to 
many  nephews,  and  as  nephew  to  many  uncles.  We 
will  therefore  (though  it  is  hardly  necessary  to  do  so) 
suppose  each  of  the  files  in  Z  to  have  been  constructed 
from  only  a  sample  consisting  of  1,000  persons,  taken  at 
random  out  of  the  more  numerous  measures  to  which  it 
refers.  By  this  treatment  Z  becomes  an  exact  Squadron, 
consisting  of  1,000  elements,  both  in  rank  and  in  file, 
and  it  is  identical  with  A  in  its  constitution,  though 
not  in  its  attitude.  The  ranks  of  Z,  which  are  Schemes, 
have  been  derived  from  the  files  of  A,  which  arc  rect- 


VII.] 


DISCUSSION  OF  THE  DATA  OF  STATURE. 


113 


angles,  therefore  the  two  Squadrons  must  stand  at  right 
angles  to  one  another,  as  in  Fig.  14.  The  upper  surface 
of  A  is  curved  in  rank,  and  horizontal  in  file ;  that  of 
Z  is  curved  in  file  and  horizontal  in  rank. 

The  Kinsmen  in  nearer  degrees  than  Z  will  be  re- 
presented by  Squadrons  whose  forms  are  intermediate 
between  A  and  Z.     Front  views  of  these  are  shown  in 


i 

FiG  .15. 

i          yi    I 

J\    !            11 

pi 

— 

vy^ 

Tr. 

T 

•¥2 


-S-1 


-1 


tis 

1 

•f- 

C       1^ 

Fig.  15.  Consequently  they  will  be  somewhat  curved 
both  in  rank  and  in  file.  Also  as  the  Kinsmen  of  all 
the  members  of  a  Population,  in  any  degree,  are  them- 
selves a  Population  having  similar  characteristics  to 
those  of  the  Population  of  w^hich  they  are  part,  it 
follows  that  the  elements  of  every  intermediate  Squadron 
when  they  are  broken  up  and  sorted  afresh  into  ordinary 
Schemes,  would  form  identical  Schemes.  Therefore,  it 
is  clear  that  a  law  exists  that  connects  the  curvatures  in 
rank  and  in  file,  of  any  Squadron.  Both  of  the  cur- 
vatures are  Curves  of  Distribution;  let  us  call  their 
Q  values  respectively  r  and  /.     Then  if  p  be  the  Q  of 

I 


114  NATURAL  INHERITANCE.  [c'Hap. 

the  general  Population,  we  arrive  at  a  general  equation 
tliat  is  true  for  all  degrees  of  Kinship  ;  namely — 

r^+/^=p^  (1) 

but  r,  tlie  curvature  in  rank,  is  a  regressed  value  of  p, 
and  may  be  written  icp,  iv  being  the  value  of  the 
Eegression.  Therefore  the  above  equation  may  be  put 
in  the  form  of 

%D''^''^P^f  (2) 

in  which  f  is  the  Q  of  the  Co-kinsmen  in  the  given 
degree. 

It  will  be  found  that  the  intersection  of  the  surfaces 
of  the  Squadrons  by  a  horizontal  plane,  whose  height  is 
equal  to  P,  forms  in  each  case  a  line,  whose  general  in- 
clination to  the  ranks  of  A  increases  as  the  Kinship 
becomes  more  remote,  until  it  becomes  a  right  angle  in 
Z.  The  progressive  change  of  inclination  is  shown  in 
the  small  squares  drawn  at  the  base  of  Fig.  13,  in  which 
the  lines  are  the  projections  of  contours  drawn  on  the 
upper  surfaces  of  the  Squadrons,  to  correspond  with  the 
multiples  there  stated  of  values  of  jy. 

It  will  be  understood  from  the  front  views  of  the 
four  different  Squadrons,  which  form  the  upper  part  of 
Fig.  13,  how  the  Mid-Statures  of  the  Kinsmen  to  the 
Men  in  each  of  the  files  of  A,  gradually  become  more 
mediocre  in  the  successive  stages  of  kinship  until  they 
all  reach  absolute  mediocrity  in  Z.  This  figure  aff*ords 
an  excellent  diagramatic  representation,  true  to  scale,- 
of  the  action  of  the  law  of  Eegression  in  Descent.  I 
should  like  to  have  given  in  addition,  a  perspective 
view    of   the    Squadrons,    but    fiiilcd    to    draw    them 


VII.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  115 

clearly,  after  making  many  attempts.  Their  curvatures 
are  so  delicate  and  peculiar  tliat  tlie  eye  can  liardly 
appreciate  them  even  in  a  model,  without  turning  it 
about  in  different  lights  and  aspects.  A  plaster  model 
of  an  intermediate  form  was  exhibited  at  the  Eoyal 
Society  by  Mr.  J.  D.  H.  Dickson,  when  my  paper  on 
Hereditary  Stature  was  read,  together  with  his  solutions 
of  the  problems  that  are  given  in  the  Appendix.  I  also 
exhibited  arrangements  of  files  and  ranks  that  were 
made  of  pasteboard.  Mr.  Dixon  mentioned  that  the 
mathematical  properties  of  a  Surface  of  Frequency 
showed  that  no  strictly  straight  line  could  be  drawn 
upon  it. 

Successive  Oenerations  of  a  People. — We  are  far  too 
apt  to  regard  common  events  as  matters  of  course,  that 
require  no  explanation,  whereas  they  may  be  problems 
of  much  interest  and  of  some  difficulty,  and  still  await 
solution. 

Why  is  it,  when  we  compare  two  large  groups  of 
persons  selected  at  random  from  the  same  race,  but 
belonging  to  different  generations,  that  they  are  usually 
found  to  be  closely  alike  ?  There  may  be  some 
small  statistical  dissimilarity  due  to  well  understood 
differences  in  the  general  conditions  of  their  lives,  but 
with  this  I  am  not  concerned.  The  present  question 
is  as  to  the  origin  of  that  statistical  resemblance  between 
successive  generations  which  is  due  to  the  strict  pro- 
cesses of  heredity,  and  which  is  commonly  observed  in 
all  forms  of  life. 

T  2 


116  NATURAL  INHERITANCE.  [chap. 

In  eacli  generation,  individuals  are  found  to  be  tall 
and  short,  heavy  and  light,  strong  and  weak,  dark 
and  pale ;  and  the  proportions  of  those  who  present 
these  several  characteristics  in  their  various  degrees, 
tend  to  be  constant.  The  records  of  geological  history 
afford  striking  evidences  of  this  statistical  similarity. 
Fossil  remains  of  plants  and  animals  may  be  dug  out  of 
strata  at  such  different  levels,  that  thousands  of  genera- 
tions must  have  intervened  between  the  periods  at  which 
they  lived  ;  yet  in  large  samples  of  such  fossils  we  may 
seek  in  vain  for  peculiarities  that  distinguish  one 
generation  from  another,  the  different  sizes,  marks,  and 
variations  of  every  kind,  occurring  with  equal  frequency 
in  all. 

If  any  are  inclined  to  reply  that  there  is  no  wonder 
in  the  matter,  because  each  individual  tends  to  leave  his 
like  behind  him,  and  therefore  each  generation  must,  as 
a  matter  of  course,  resemble  the  one  preceding,  the 
patent  fact  of  Eegression  shows  that  they  utterly 
misunderstand  the  case. 

We  have  now  reached  a  stage  at  which  it  has 
become  possible  to  discuss  the  problem  with  some 
exactness,  and  I  will  do  so  by  giving  mathematical 
expression  to  what  actually  took  place  in  the  Statures 
of  that  sample  of  our  Population  whose  life-histories 
are  recorded  in  the  E.F.F.  data. 

The  Males  and  Females  in  Generation  I.  whose  M  has 
the  value  of  P  (viz.,  GSj  inches),  and  whose  Q  is  17 
inch,  were  found  to  group  themselves  as  it  were  at 
random,    into  couples,   and  then  to  form  a  system  of 


VII.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  117 

Mid-Parents.  This  system  had  of  course  the  same  IVI 
as  the  general  Population,  but  its  Q  was  reduced  to 
^^xl'7  inch,  or  to  1*2  inch.  It  was  next  found 
w^hen  the  Statures  of  the  Mid-Parents,  expressed  in  tlie 
form  of  P-h(=tD),  were  sorted  into  groups  in  which 
D  w^as  the  same  (reckoning  to  the  nearest  inch),  that  a 
Co-fraternity  sprang  from  each  group,  and  that  its  IVI 
had  the  value  of  P-l-(zizfD).  The  system  in  which 
each  element  is  a  Mid- Co-Fraternity,  must  have  the 
same  M  as  before,  of  6  8|^  inches,  but  its  Q  will  be  again 
reduced,  namely  from  1  '2  inch  to  f  x  1  *2  inch,  or  to 
0'8  inch.  Lastly,  the  individual  Co-Fraternals  were 
seen  to  be  dispersed  from  their  respective  Mid-Co- 
Fraternities,  with  a  Q  equal  in  each  case  to  1*5  inch. 
The  sum  of  all  of  the  Co-Fraternals  forms  the  Popula- 
tion of  Generation  11.  Consequently  the  members  of 
Generation  II.  constitute  a  system  that  has  an  IVI  of 
68^  inches  and  a  Q  equal  to  ^  [(0-8)'-|- (1'5)'],  =  17 
inch.  These  values  are  identical  with  those  in  Genera- 
tion I.  ;  so  the  cause  of  their  statistical  similarity  is 
tracked  out. 

There  ought  to  be  no  misunderstanding  as  to  the 
character  of  the  evidence  or  of  the  reasoning  upon 
which  this  analysis  is  based.  A  small  but  fair  sample 
of  the  Population  in  two  successive  Generations  has  been 
taken,  and  its  conditions  as  regards  Stature  have  been 
strictly  discussed.  It  was  found  that  the  distribution 
of  Stature  was  sufficiently  Normal  to  justify  our  ignoring 
any  shortcomings  in  that  respect.     The  transmutation 


118  NATURAL  INHERITANCE.  [chap 

of  female  lieigiits  to  tlieir  male  equivalents  was  justified 
by  the  fact  that  when  the  individual  Statures  of  a  group 
of  females  are  raised  in  the  proportion  of  100  to  108, 
the  Scheme  drawn  from  them  fairly  coincides  with  that 
drawn  from  male  Statures.  Marriage  selection  was  found 
to  take  no  sufiicient  notice  of  Stature  to  be  worth  con- 
sideration ;  neither  was  the  number  of  children  in 
Fraternities  found  to  be  sensibly  afi^ected  by  the 
Statures  of  their  Parents.  Again,  it  was  seen  to  be 
of  no  consecj^uence  when  dealing  statistically  with  the 
offspring,  whether  their  Parents  were  alike  in  stature  or 
not,  the  only  datum  deserving  consideration  being  the 
Stature  of  the  Mid-Parent,  that  is  to  say,  the  average 
value  of  (l)  the  Stature  of  the  Father,  and  of  (2)  the 
Transmuted  Stature  of  the  Mother.  I  fully  grant  that 
not  one  of  these  deductions  may  be  strictly  exact,  but 
the  error  introduced  into  the  conclusions  by  supposing 
them  to  be  correct  proves  not  to  be  worth  taking  into 
account  in  a  first  approximation. 

Precisely  the  same  may  be  said  of  the  ulterior  steps 
in  this  analysis.  Every  one  of  them  is  based  on  the 
properties  of  an  ideally  perfect  curve,  but  in  no  case 
has  there  been  need  to  make  any  sensible  departure 
from  the  observed  results,  except  in  assigning  a  uniform 
value  to  Q  in  the  difi"erent  Co-Fraternities.  Strictly 
speaking,  that  value  was  found  to  slightly  rise  or  fall  as 
the  Mid-Stature  of  the  Co-Fraternity  rose  or  fell.  This 
suggested  the  advisability  of  treating  the  whole  inquiry 
on  the  principle  of  the  Geometric  Mean,  Appendix  G. 
I  tried  that  principle  in  what  seemed  to  be  the  most 


VII.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  .     119 

hopeful  case  among  my  18  schemes,  but  found  the  gain, 
if  any,  to  be  so  small,  that  I  did  not  care  to  go  on 
with  the  experiment.  It  did  not  seem  to  deserve  the 
additional  trouble,  and  I  was  indisposed  to  do  anything 
that  was  not  really  necessary,  which  might  further 
confuse  the  reader.  But  had  I  possessed  better  data, 
I  should  have  tried  the  Geometric  Mean  throughout. 
In  doing  so,  every  measure  would  be  replaced  by  its 
logarithm,  and  these  logarithms  would  be  treated  just 
as  if  they  had  been  the  observed  values.  The  conclusions 
to  which  they  might  lead  would  then  be  re-transmuted 
to  the  numbers  of  which  they  were  the  logarithmic 
equivalents. 

In  short,  we  have  dealt  mathematically  with  an  ideal 
population  which  has  similar  characteristics  to  those  of 
a  real  population,  and  have  seen  how  closely  the' 
behaviour  of  the  ideal  population  corresponds  in  every 
stage  to  that  of  the  real  one.  Therefore  we  have 
arrived  at  a  closely  approximate  solution  of  the  problem 
of  statistical  constancy,  though  numerous  refinements 
have  been  neglected. 

Natural  Selection. — This  hardly  falls  within  the 
scope  of  our  incjuiry  into  Natural  Inheritance,  but  it 
will  be  appropriate  to  consider  briefly  the  way  in 
which  the  action  of  Natural  Selection  may  harmonise 
with  that  of  pure  heredity,  and  work  together  with  it 
in  such  a  manner  as  not  to  compromise  the  normal 
distribution  of  faculty.  To  do  this,  we  must  deal 
with  the  case  that  best  represents  the  various  possible 


120  NATURAL  INHERITANCE.  [chap. 

occurrences,  namely  tliat  in  wliicli  tlie  mediocre  members 
of  a  population  are  those  tliat  are  most  nearly  in 
harmony  with  their  circumstances.  The  harmony  ought 
to  concern  the  aggregate  of  their  faculties,  combined 
on  the  principle  adopted  in  Table  3,  after  weighting 
them  in  the  order  of  their  importance.  We  may  deal 
with  any  faculty  separately,  to  serve  as  an  example,  if 
its  mediocre  value  happens  to  be  that  which  is  most 
preservative  of  life  under  the  majority  of  circumstances. 
Such  is  Stature,  in  a  rudely  approximate  degree,  inas- 
much as  exceptionally  tall  or  exceptionally  short  persons 
have  less  chance  of  life  than  those  of  moderate  size. 

It  will  give  more  definiteness  to  the  reasoning  to 
take  a  definite  example,  even  though  it  be  in  part  an 
imaginary  one.  Suppose  then,  that  we  are  considering 
the  stature  of  some  animal  that  is  liable  to  be  hunted 
by  certain  beasts  of  prey  in  a  particular  country.  So 
far  as  he  is  big  of  his  kind,  he  would  be  better  able 
than  the  mediocrities  to  crush  through  thick  grass  and 
foliage  whenever  he  was  scampering  for  his  life,  to  jump 
over  obstacles,  and  possibly  to  run  somewhat  faster 
than  they.  So  far  as  he  is  small  of  his  kind,  he  would 
be  better  able  to  run  through  narrow  openings,  to 
make  quick  turns,  and  to  hide  himself.  Under  the 
general  circumstances,  it  would  be  found  that  animals 
of  some  particular  stature  had  on  the  whole  a  better 
chance  of  escape  than  any  other,  and  if  their  race  is 
closely  adapted  to  their  circumstances  in  respect  to 
stature,  the  most  favoured  stature  would  be  identical 
with  the  M  of  the  race.     AVe  already  know  that  if  we 


VII.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  121 

call  this  value  P,  and  write  each  stature  under  the 
form  of  P  +  o^  (in  which  x  includes  its  sign),  and  if  the 
number  of  times  with  which  any  value  P  +  cc  occurs, 
compared  to  the  number  of  times  in  which  P  occurs, 
be  called  y,  then  x  and  y  are  connected  by  the  law 
of  Frequency  of  Error. 

Though  the  impediments  to  flight  are  less  unfavour- 
able, on  the  average,  to  the  stature  P  than  to  any  other, 
they  will  differ  in  different  experiences.  The  course  of 
one  animal  may  chance  to  pass  through  denser  foliage 
than  usual,  or  the  obstacles  in  his  way  may  be  higher. 
In  that  case  an  animal  whose  stature  exceeded  P  would 
have  an  advantage  over  mediocrities.  Conversely,  the 
circumstances  might  be  more  favourable  to  a  small 
animal. 

Each  particular  line  of  escape  w^ould  be  most  favour- 
able to  some  particular  stature,  and  whatever  the  value 
of  X  might  be,  it  is  possible  that  the  stature  V-{-x 
might  in  some  cases  be  more  favoured  than  any  other. 
But  the  accidents  of  foliage  and  soil  in  a  country  are 
characteristic  and  persistent,  and  may  fairly  be  con- 
sidered as  approximately  of  a  typical  kind.  Therefore 
those  that  most  favour  the  animals  whose  stature  is 
P  will  be  more  frequently  met  with  than  those  that 
favour  any  other  stature  P-l-x,  and  the  frequency 
of  the  latter  occurrence  will  diminish  rapidly  as  x 
increases.  If  the  number  of  times  with  which  any 
particular  value  oiV-\-x  is  most  favoured,  as  compared 
with  the  number  of  times  in  which  P  is  most  favoured, 
be  called  y\  we  may  fairly  assume  that  y^  and  x  are 


122  NATURAL  INHERITANCE.  [chap. 

connected  by  the  law  of  Frequency  of  Error.  But 
though  the  system  of  y  values  and  that  of  if  values 
may  be  both  subject  to  the  law,  it  is  not  for  a  moment 
to  be  supposed  that  their  Q  values  are  necessarily 
the  same. 

We  have  now  to  show  how  a  large  population  of 
animals  becomes  reduced  by  the  action  of  natural 
selection  to  a  smaller  one,  in  which  the  M  value  of  the 
statures  is  unchanged,  while  the  Q  value  is  decreased. 

To  do  this  we  must  first  consider  the  population  to 
have  grown  up  entirely  shielded  from  causes  of  pre- 
mature mortality  ;  call  their  number  N.  Then  suppose 
them  to  be  assailed  by  all  the  lethal  influences  that  have 
no  reference  to  stature.  These  would  reduce  their 
number  to  W,  but  by  the  hypothesis,  the  values  of 
M  and  of  Q  would  remain  unaffected.  Next  let  the 
influences  that  act  selectively  on  stature,  further  reduce 
the  numbers  to  S ;  these  being  the  final  survivors. 
We  have  seen  that  : — 

^=:the  number  of  individuals  who  have  the  stature 
Pzh^,  counting  those  who  have  the  stature  P,  as  1. 

?/'  =  the  number  of  times  in  which  Pzb^  is  the  most 
favoured  stature,  counting  those  in  which  P  is  the 
most  favoured,  as  1. 

Then  yij —  t]iQ  number  of  times  that  individuals  of 
the  stature  Pzba^  are  selected,  counting  those  in  which 
individuals  of  the  stature  P  are  selected,  as  1. 

As  the  relation  between  y  and  x,  and  between  y'  and 
X  are  severally  governed  by  the  law  of  Frequency  of 
Error,  it  follows  directly  from  the   formula   by  which 


VII.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  123 

that  law  is  expressed,  that  the  relation  between  yy^  and 
X  is  also  governed  by  it.  The  value  of  P  of  course 
remains  the  same  throughout,  but  the  Q  in  the  system 
of  yy'  values  is  necessarily  less  than  that  in  the  system 
of  y  values. 

It  might  well  be  that  natural  selection  would  favour 
the  indefinite  increase  of  numerous  separate  faculties,  if 
their  improvement  could  be  effected  without  detriment 
to  the  rest ;  then,  mediocrity  in  that  faculty  would 
not  be  the  safest  condition.  Thus  an  increase  of 
fleetness  would  be  a  clear  gain  to  an  animal  liable  to 
be  hunted  by  beasts  of  prey,  if  no  other  useful  faculty 
was  thereby  diminished. 

But  a  too  free  use  of  this  *Mf"  would  show  a 
jaunty  disregard  of  a  real  difficulty.  Organisms  are 
so  knit  together  that  change  in  one  direction  involves 
change  in  many  others  ;  these  may  not  attract  atten- 
tion, but  they  are  none  the  less  existent.  Organisms  are 
like  ships  of  war  constructed  for  a  particular  purpose 
in  warfare,  as  cruisers,  line  of  battle  ships,  &c.,  on  the 
principle  of  obtaining  the  utmost  efficiency  for  their 
special  purpose.  The  result  is  a  compromise  between 
a  variety  of  conflicting  desiderata,  such  as  cost,  speed, 
accommodation,  stability,  weight  of  guns,  thickness  of 
armour,  quick  steering  power,  and  so  on.  It  is  hardly 
possible  in  a  ship  of  any  long  established  type  to  make 
an  improvement  in  any  one  of  these  respects,  without  a 
sacrifice  in  other  directions.  If  the  fleetuess  is  increased, 
the  engines  must  be  larger,  and  more  space  must  be 
given  up  to  coal,  and  this  diminishes  the   remaining 


124  NATURAL  INHERITANCE.  [chap. 

accommoda,tion.  Evolution  may  produce  an  altogether 
new  type  of  vessel  that  shall  be  more  efficient  than  the 
old  one,  but  when  a  particular  type  of  vessel  has  become 
adapted  to  its  functions  through  long  experience  it  is  not 
possible  to  produce  a  mere  variety  of  its  type  that  shall 
have  increased  efficiency  in  some  one  particular  without 
detriment  to  the  rest.     So  it  is  with  animals. 

Variability  in  Fraternities. — Human  Fraternities  are 
far  too  small  to  admit  of  their  Q  being  satisfactorily 
measured  by  the  direct  method.  We  are  obliged  to 
have  recourse  to  indirect  methods,  of  which  no  less  than 
four  are  available.  I  shall  ajoply  each  of  them  to  both 
the  Special  and  to  the  E.F.F.  data  ;  this  mil  give  8 
separate  estimates  of  its  value,  which  in  the  meantime 
will  be  called  h.     The  four  methods  are  as  follow : 

First  method ;  by  Fraternities  each  containing  the 
same  nnmber  of  persons  : — Let  me  begin  by  saying  that 
I  had  already  found  in  the  large  Fraternities  of  Sweet 
Peas,  that  the  sizes  of  individuals  of  whom  they  con- 
sisted were  normally  distributed,  and  that  their  Q  was 
independent  of  the  size,  or  of  the  Stature  as  we  may 
phrase  it,  of  the  Mid- Fraternity.  We  have  also  seen 
that  the  Q  is  practically  the  same  in  all  Co-fraternities 
of  men.  Therefore  it  is  reasonable  to  expect  that  it 
will  also  be  found  to  be  the  same  in  all  their  Fraternities, 
though  owing  to  their  small  size  we  cannot  assure  our- 
selves of  the  fact  by  direct  evidence.  We  will  assume 
this  to  be  the  case  for  the  present ;  it  will  be  seen  that 
the  results  justify  the  assumption. 


VII.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  125 

The  value  of  the  IVI  of  a  small  Fraternity  may  be 
much  affected  by  the  addition  or  subtraction  even  of 
a  single  member,  it  may  therefore  be  called  the  apparent 
M,  to  be  distinguished  from  the  triie  ^,  from  which  its 
members  would  be  found  to  be  dispersed,  if  there  had 
been  many  more  of  them.  The  apparent  M  approxi- 
mates towards  the  true  M  as  the  Fraternity  increases 
in  size,  though  at  a  much  slower  rate.  We  have  now 
somehow  to  get  at  this  true  M.  For  distinction  and 
for  brevity  let  us  call  the  apparent  IV!  of  any  small 
Fraternity  (MF^),  and  that  of  the  corresponding  true 
IVI  (MF).  Then  (MF)  may  be  deduced  from  (MF')  as 
follows  : — 

We  will  begin  by  allowing  ourselves  for  the  moment 
to  imagine  the  existence  of  an  exceedingly  large  Frater- 
nity, far  more  numerous  than  is  physiologically  possible, 
and  to  suppose  that  its  members  vary  among  themselves 
just  as  widely,  neither  more  nor  less  so,  than  in  the 
small  Fraternities  of  real  life.  The  (MF^)  of  our  large 
ideal  Fraternity  will  therefore  be  identical  with  its  (MF), 
and  its  Q  will  be  the  same  as  h.  Next,  take  at  random 
out  of  this  huge  ideal  Fraternity  a  large  number  of  small 
samples,  each  consisting  of  the  same  number,  n,  of 
brothers,  and  call  the  apparent  Mid- values  in  the  several 
samples,  (MF^i),  (MF^s)?  &c.  It  can  easily  be  shown 
that  (MF^i),  (MF^g)?  &c.,  will  be  so  distributed  about  the 
common  centre  of  (MF),  that  the  Prob.  Deviation  of 
any  one  of  them  from  it,  that  is  to  say,  the  Q  of  their 
system  will  =  7>  x  ^.  If  n  =  1 ,  then  the  Prob.  Devia- 
tion  becomes    6,    as   it   should.     If  n  =  2,   the  Prob. 


126  NATURAL  INHERITANCE.  [chap. 

Deviation  is  determined  by  tlie  same  problem  as  tbat 
wliich  concerned  tbe  Q  of  the  Mid-Parentages  (page  87), 
where  it  was  shown  to  be  h  x  ~^.  By  similar  reasoning, 
when  72  =  3,  the  Prob.  Deviation  becomes  ^  x  -^,  and 
so  on.  When  n  is  infinitely  large,  the  Prob.  Deviation 
is  0  ;  that  is  to  say,  the  (MF^)  values  do  not  differ  at 
all  from  their  common  (MF). 

Now  if  we  make  a  collection  of  human  Fraternities, 
each  consisting  of  the  same  number,  n,  of  brothers,  and 
note  the  differences  between  the  (MF^)  in  each  frater- 
nity and  the  individual  brothers,  we  shall  obtain  a 
system  of  values.  By  drawing  a  Scheme  from  these  in 
the  usual  way,  we  are  able  to  find  their  Q ;  let  us  call 
it  d.  We  then  determine  h  in  terms  of  d,  as  follows  : — 
The  (MF^)  values  are  distributed  about  their  common 
(MF),  each  with  the  Prob.  Deviation  of  h  x  ^^^,  and  the 
Statures  of  the  individual  Brothers  are  distributed 
about  their  respective  (MF^)  values,  each  with  the  Prob. 
Deviation  d.  The  compound  result  is  the  same  as 
if  the  statures  of  the  individual  brothers  had  been 
distributed  about  the  common  (MF),  each  with  the 
Prob.  Deviation  h, 

consequently  5^  =  (i^  -}-  — ,    or  lf= d^. 

^  ^  n'  n-1 

I  determined  d  by  observation  for  four  different 
values  of  n,  having  taken  four  groups  of  Fraternities, 
consisting  respectively  of  4,  5,  6,  and  7  brothers,  as 
shown  in  Table  14.  Substituting  these  four  observed 
values  in  turns  for  d  in  the  above  formula,  I  obtained 


VII.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  127 

four  independent  values    of   h,  wliich    are  respectively 
I'Ol,  1-01,  1'20,  and  I'OS  ;  tlie  mean  of  these  is  1'07. 

Second  Method ;  from  the  mean  value  of  Fraternal 
Eegression : — We  may  look  on  the  Population  as  com- 
posed of  a  system  of  Fraternities.  Call  their  respective 
true  centres  (see  last  paragraph)  (MFi),  (MFg),  &c. 
These  will  be  distributed  about  P  with  an  as  yet  un- 
known Prob.  Deviation,  that  we  will  call  c.  The 
individual  members  of  each  Fraternity  will  of  course 
be  distributed  from  their  own  (MF)  with  a  Q  equal  to  h. 
Then  {l'7Y  =  c'  +  ¥  (l) 

Let  P-l-(dzF„)  be  the  stature  of  any  individual,  and 
let  P+(dzMF,,)  be  that  of  the  M  of  his  Fraternity, 
then  Problem  4  (page  69)  shows  us  that  : — 

,    , ,       ,        ^  (MFJ  .  c'  ,  , 

the  most  probable  value  oi   —^ — -  is  ^^,2  ,    2  (2) 

This  is  also  the  value  of  Fraternal  Eegression,  and 
therefore  equal  to  -f.  Substituting  in  (2),  and  replacing 
c  by  the  value  given  by  (l),  we  obtain  6=:  0*9 8 
inch. 

Third  Method ;  by  the  Variability  in  the  value  of 
individual  cases  of  Fraternal  Eegression  : — The  figures 
in  each  line  of  Table  13  are  found  to  have  a  Q  equal  to 
1  '24  inch,  and  they  are  the  results  of  two  independent 
systems  of  variation.  First,  the  several  (MF)  values  (see 
last  paragraph)  are  dispersed  from  the  M  of  all  of 
them  with    a    Q    that  we  will  call  v.      Secondly   the 


128  NATURAL  INHERITANCE.  [chap. 

individiial   brotliers   in    each   Fraternity  are    dispersed 
from  their  own  (MF)  with  a  Q  equal  to  h. 
Hence  {l'24.Y==v'-]-h\ 

he 

But  it  is  shown  Problem  5  that  v  =  ,/,2  , — 2\  J 

7  2    2 

therefore  (1-24)^  =  6^  +  5^. 

Substituting  for  c^  its  value  of  (17)^  —  6^  (see  last  para- 
graph), we  obtain  5  =  0*98  inch. 

Fourth  Method  ;  from  differences  between  pairs  of 
brothers  taken  at  random : — In  the  fourth  method, 
Pairs  of  Brothers  are  taken  at  random,  and  the  Differ- 
ences between  the  statures  in  each  pair  are  noted  ;  then, 
under  the  following  reservation,  any  one  of  these 
differences  would  have  the  Prob.  value  of  \/  2  x  5.  The 
reservation  is,  that  only  as  many  Differences  should  be 
taken  out  of  each  Fraternity  as  are  independent.  A 
Fraternity  of  n  brothers  admits  of  '-^^^  possible  pairs, 
and  the  same  number  of  Differences  ;  but  as  no  more 
than  n—1  of  these  are  independent,  that  number  only 
of  the  Differences  should  be  taken.  I  did  not  appre- 
ciate this  necessity  at  first,  and  selected  pairs  of  brothers 
on  an  arbitrary  system,  which  had  at  all  events  the 
merit  of  not  taking  more  than  four  sets  of  Differences 
from  any  one  Fraternity  however  large  it  might  be. 
It  was  faulty  in  taking  three  Differences  instead  of  only 
two,  out  of  a  Fraternity  of  three  brothers,  and  four 
Differences,  instead  of  only  three,  from  a  Fraternity  of 


VII.] 


DISCUSSION  OF  THE  DATA  OF  STATURE. 


129 


four  brothers,  and  therefore  givang  an  increased  weight 
to  those  Fraternities,  but  in  other  respects  the  system 
was  hardly  objectionable.  The  introduced  error  must 
be  so  slight  as  to  make  it  scarcely  worth  while  now  to 
go  over  the  work  again.  By  the  system  adopted,  I 
found  the  Prob.  Difference  to  be  1'55,  which  divided 
by  \^  2  gives  h  =1'10  inch. 

Thus  far  we  have  dealt  with  the  special  data  only. 
The  less  trustworthy  R.F.F.  give  larger  values  of  b  in 
every  case.  An  epitome  of  all  the  results  appears  in 
the  following  table  : — 


Methods  and  data. 

Values  of  h  obtained  by  different  methods 
and  from  different  data. 

From  Special  Data. 

From  R.F.F.  data.l 

(1)  From   Fraternities   each 
containing  the  same  number  of 
persons     

1-07 
0-98 
MO 
MO 

1-38 
1-31 
M4 
1-35 

(2)  From  the  mean  value  of 
Fraternal  Regression 

(3)  From  the  Variability  cf 
Fraternal  Regression 

(4)  From  Pairs  of  Brothers 
taken  at  random 

Mean. 

1-06 

The   data  used  in   the  four  methods  are  somewhat 
different.     In  (1)  I  could  not  deal  with  small  Fraterni- 

1  The  E.F.F.  results  were  obtained  from  brothers  only  and  not  from 
transmuted  sisters,  except  in  method  (2),  where  the  paucity  of  the  data 
compelled  me  to  include  them, 

K 


130  NATURAL  INHERITANCE.  [ciiAr. 

ties,  so  all  were  disregarded  tliat  contained  fewer  tlian 
four   individuals.      In   (2)    and  (3)   I    could,  not   with, 
safety  use   large  Fraternities.      In  (4)  the   method  of 
selection  was,  as  we  have  seen,  quite  indifferent.     This 
makes  the  accordance  of  the  results  derived  from  the 
Special  data  all  the  more  gratifying.     Those  from  the 
E.F.F.   data   accord   less   well   together.      The   E.F.F. 
measures   are   not   sufficiently  exact   for   use  in  these 
delicate  calculations.     Their  results,  being  compounded 
of  b  and  of  their  tendency  to  deviate  from  exactness, 
are  necessarily  too  high,  and  should  be  discarded.     I 
gather  from   all  this  that  we  may  safely  consider  the 
value  of  h  to  be  less  than  1'06,  and  that  allowing  for 
some  want  of  precision  in  the   Special  data,  the  very 
convenient    value    of    1*00    inch    may    reasonably   be 
adopted. 

Trustivorthiness  of  the  Constants. — There  is  difficulty 
in  correcting  the  results  obtained  from  the  E.F.F.  data, 
though  we  can  make  some  estimate  of  their  general 
inaccuracy  as  compared  with  the  Special  data.  The 
reason  of  the  difficulty  is  that  the  inaccuracy  cannot 
be  ascribed  to  an  uncertainty  of  equal  ±  amount  in 
every  entry,  such  as  might  be  due  to  a  doubt  of 
"shoes  off"  or  ''shoes  on."  If  it  were  so,  the  Prob. 
Error  of  a  single  value  of  the  E.F.F.  would  be  greater 
than  that  of  one  of  the  Specials,  whereas  it  proves  to 
be  the  same.  It  is  likely  that  the  inaccuracy  is  a  com- 
pound first  of  the  uncertainty  above  mentioned,  whose 
effect  would  be  to  increase  the  value  of  the  Prob.  Error, 


VII  ]  DISCUSSION  OF  THE  DATA  OF  STATURE.  131 

and  secondly  of  a  tendency  on  tlie  part  of  my  corre- 
spondents to  record  medium  statures  when  they  were 
in  doubt,  whose  effect  would  be  to  reduce  the  value  of 
the  Prob.  Error,  The  E.F.R  data  in  Table  12  run  so 
irregularly  that  I  cannot  interpret  them  with  aDy 
assurance.  The  value  they  give  for  Fraternal  Eegression 
certainly  does  not  exceed  ^,  and  therefore  a  correction, 
amounting  to  no  less  than  ^  of  its  amount,  is  required 
to  bring  it  to  a  parity  with  that  derived  from  the 
Special  data  (because  i-  +  ^  x  -J-  =  f).  Hence  it 
might  be  argued,  that  the  value  of  Eegression  from 
Mid-Parent  to  Son,  which  the  E.F.F.  data  gave  as  f, 
ought  to  receive  a  similar  correction.  If  so,  it  would 
be  raised  to  |-  -i-  -|  =  f ;  but  I  cannot  believe  this 
high  value  to  be  correct.  My  first  estimate  made 
from  the  E.F.F.  data,  was  f ,  as  already  mentioned.  If 
this  be  adopted,  the  corrected  value  would  be  f ,  or  ^ 
instead  of  f ,  which  might  possibly  pass.  Curiously 
enough,  this  value  of  ^  for  Eegression  from  Mid-Parent 
to  Son,  coincides  with  the  value  of  f  for  Eegression 
from  a  single  Parent  to  Son,  which  the  direct  observa- 
tions showed  (see  page  99),  but  which  owing  to  their 
paucity  and  to  the  irregularity  of  the  way  in  which 
they  ran,  I  rejected  and  still  reject,  at  least  for  the 
present.  While  sincerely  desirous  of  obtaining  a 
revised  value  of  average  Filial  Eegression  from  entirely 
different  and  more  accurate  groups  of  data,  the  pro- 
visional value  already  adopted  of  f  from  Mid- Parent 
to  Son  may  be  accepted  as  being  near  enough  for  the 
present.     It  is  impossible  to  revise  one  datum  in  the 

k2 


132  NATURAL  INHERITANCE.  [chap. 

E.F.F.  series  without  revising  all,  as  they  hang  together 
and  support  one  another. 

General  View  of  Kinship. — We  are  now  able  to  deal 
with  the  distribution  of  statures  among  the  Kinsmen  in 
every  near  degree,  of  persons  whose  statures  we  know, 
but  whose  ancestral  statures  we  either  do  hot  know,  or 
do  not  care  to  take  into  account.  We  are  able  to  calcu- 
late Tables  for  every  near  degree  of  Kinship  on  the  form 
of  Table  11,  and  to  reconstruct  that  same  Table  in  a 
shape  free  from  irregularities.  We  must  first  find  the 
Regression,  which  we  may  call  w,  appropriate  to  the 
degree  of  Kinship  in  question.  Then  we  calculate  a 
value  f  for  each  line  of  a  Table  corresponding  in  form  to 
that  of  Table  11,  in  which/* was  found  to  be  equal  to 
1*50  inch.  We  deduce  the  value  of  y  from  that  of  w  by 
means  of  the  general  equation  pV-{-f^=p^,  p  being 
equal  to  1*7  inch.  The  values  to  be  inserted  in  the 
several  lines  are  then  calculated  from  the  ordinary  table 
(Table  5)  of  the  "probability  integral." 

As  an  example  of  the  first  part  of  the  process,  let  us 
suppose  we  are  about  to  construct  a  table  of  Uncles  and 
their  Nephews,  we  find  w  and  f  as  follows  :  A  Nephew 
is  the  son  of  a  Brother,  therefore  in  this  case  we  have 
t(;r=ixf=:f ;  whence /=  1*66. 

The  Regression,  which  we  call  lu,  is  a  convenient  and 
correct  measure  of  family  likeness.  If  the  resemblance 
of  the  Kinsman  to  the  Man,  was  on  the  average  as 
perfect  as  that  of  the  Man  to  his  own  Self,  there  would 
be  no  Regression  at  all,  and  the  value  of  lo  would  be  1. 


VII.J 


DISCUSSION  OF  THE  DxVTA  OF  STATURE. 


133 


Table    of    Data  for  calculating    Tables    of    Distribution    of 
Stature  among  the  Kinsmen  of  Persons  whose    Stature  is 

KNOWN. 


From  group  of  persons  of  the  same  Stature, 
to  their  Kinsmen  in  various  near  degrees. 

Mean 
regression=w. 

Q  =  f 

=  PXV(1-W2). 

Mid-parents  to  Sons 

2/3 
2/3 

1/3 

2/9 

1/9 

2/27 

1-27 
1-27 

1-60 

1-66 

^    Practically 
J  that  of  Popu- 
)      lation,  or 
(       1'7  inch. 

Brothers  to  Brothers    

Fathers  or  Sons  to  "1 

Sons  or  Fathers        j 

Uncles  or  Nephews  to  ) 
Nephews  or  Uncles     j     

Grandsons  to  Grandparents... 
Cousins  to  Cousins    

On  the  other  hand,  if  the  Kinsmen  were  on  the  average 
no  more  like  the  Man  than  if  they  had  been  a  group 
picked  at  random  out  of  the  general  Population,  then 
the  Eegression  to  P  would  be  complete.  The  IVI  of  the 
Kinsmen,  which  is  expressed  by  P  +  t(^(dzD),  would  in 
that  case  become  P,  whatever  might  have  been  the  value 
of  D  ;  therefore  w  must  =  0.  We  see  by  the  preceding 
Table  that  as  a  general  rule.  Fathers  or  Sons  should  be 
held  to  be  only  one-half  as  near  in  blood  as  Brothers, 
and  Uncles  and  Nephews  to  be  one- third  as  near  in 
blood  as  Brothers.  Cousins  are  4-|^  times  as  remote  as 
Fathers  or  as  Sons,  and  9  times  as  remote  as  Brothers. 
I  do  not  extend  the  table  further,  because  considera- 
tions would  have  to  be  taken  into  account  that  will  be 
discussed  in  the  next  Section. 

The    remarks   made    in   a   previous   chapter    about 


134  NATURAL  INHERITANCE.  [chap. 

heritages  tliat  blend  and  those  that  are  mutually  exclu- 
sive, must  be  here  borne  in  mind.  It  would  be  a  poor 
prerogative  to  inherit  say  the  fifth  part  of  the  peculiarity 
of  some  gifted  ancestor,  but  the  chance  of  1  to  5,  of 
inheriting  the  whole  of  it,  would  be  deservedly  prized. 

Separate  Contribution  of  each  Ancestor. — In  making 
the  statement  that  Mid-Parents  whose  Stature  is  P±D 
have  children  whose  average  stature  is  PzhfD,  it  is 
supposed  that  no  separate  account  has  been  taken  of 
the  previous  ancestry.  Yet  though  nothing  may  be 
known  of  them,  something  is  tacitly  impKed  and  has 
been  tacitly  allowed  for,  and  this  requires  to  be  elimi- 
nated before  we  can  learn  the  amount  of  the  Parental 
bequest,  pure  and  simple.  What  that  something  is,  we 
must  now  try  to  discover.  When  speaking  of  converse 
Eegression,  it  was  shown  that  a  peculiarity  in  a  Man 
implied  a  peculiarity  of  J-  of  that  amount  in  his  Mid- 
Parent.  Call  the  peculiarity  of  the  Mid-Parent  D,  then 
the  implied  peculiarity  of  the  Mid-Parent  of  the  Mid- 
Parent,  that  is  of  the  Mid- Grand-Parent  of  the  Man, 
would  on  the  above  supposition  be  J^D,  that  of  the  Mid- 
Great- Grand- Parent  would  be  ^D,  and  so  on.  Hence 
the  total  bequeathable  property  would  amount  to 
I>(l+i  +  i  +  &c.)=Df. 

Do  the  bequests  from  each  of  the  successive  genera- 
tions reach  the  child  without  any,  or  what,  diminution 
by  the  way  ?  I  have  not  sufficient  data  to  yield  a  direct 
reply,  and  must  therefore  try  limiting  suppositions. 

First,  suppose  the  bequests  by  the  various  generations 


VII.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  135 

to  be  equally  taxed ;  then,  as  an  accumulation  of  ances- 
tral contributions  whose  sum  amounts  to  Df  yields  an 
effective  heritage  of  only  Df,  it  follows  that  each  piece 
of  heritable  property  must  have  been  reduced  to  f  of  its 
original  amount,  because  f  x  f  =  §. 

Secondly,  suppose  the  tax  not  to  be  uniform,  but  to 
be  repeated  at  each  successive  transmission,  and  to  be 

equal  to  -  of  the  amount  of  the  property  at  each 
stage.  In  this  case  the  effective  heritage  would  be 
I^  I  -  +  TT^  +  7^2^ ^ —  )  =  I) ,    which     must,     as 

before,  be  equal  to  Dl- :    whence  -  =  — 
^  ^  r       11 

Thirdly,  it  might  possibly  be  supposed  that  the  Mid- 
Ancestor  in  a  remote  generation  should  on  the  average 
contribute  more  to  the  child  than  the  Mid-Parent,  but 
this  is  quite  contrary  to  what  is  observed.  The  descend- 
ants of  what  was  "  pedigree  wheat,"  after  being  left  to 
themselves  for  many  generations,  show  little  or  no  trace 
of  the  remarkable  size  of  their  Mid- Ancestors  in  the 
generations  just  before  they  were  left  to  themselves, 
though  the  offspring  of  those  Mid-Ancestors  in  the  first 
generation  did  so  unmistakably. 

The  results  of  our  only  two  valid  limiting  suppositions 
are  therefore,  (l)  that  the  Mid-Parental  peculiarities, 
pure  and  simple,  influence  the  offspring  to  ^  of  their 
amount ;  (2)  that  they  influence  it  to  ^  of  their  amount. 
These  values  differ  but  slightly  from  ^,  and  their  mean 
is  closely  -|,  so  we  may  fairly  accept  that  result.     Hence 


136  NATURAL  INHERITANCE.  [chap. 

tlie  influence,  pure  and  simple,  of  the  Mid-Parent  may 
be  taken  as  ^,  and  that  of  tlie  Mid- Grand- Parent  as  ^, 
and  so  on.  Consequently  the  influence  of  the  individual 
Parent  would  be  ^,  and  of  the  individual  Grand-Parent 
^,  and  so  on.  It  would,  however,  be  hazardous  on  the 
present  slender  basis,  to  extend  this  sequence  with  con- 
fidence to  more  distant  generations. 

Pedigree  Moths. — I  am  endeavouring  at  this  moment 
to  obtain  data  that  will  enable  me  to  go  further,  by  breed- 
ing Pedigree  Moths,  thanks  to  the  aid  of  Mr.  Frederick 
Merrifield.    The  moths  Selenia  Illustraria  and  Illunaria 
are  chosen  for  the  purpose,  partly  on  account  of  their  being 
what  is  called  double  brooded ;  that  is  to  say,  they  pass 
normally  through  two  generations  in  a  single  year,  which 
is  a  great  saving  of  time  to  the  experimenter.     They  are 
hardy,  prolific  and  variable,  and  are  found  to  stand  chloro- 
form well,  previously  to  being  measured  and  then  paired. 
Every  mfember  of  each  Fraternity  is  preserved  along 
three  lines  of  descent — one  race  of  long-winged  moths, 
one  of  medium-winged,  and  one  of  short- winged  moths. 
The  three  parallel  sets  are  reared  under  identical  con- 
ditions, so  that  the  medium  series  supplies  a  trustworthy 
relative   base,  from  which   to   measure   the  increasing 
divergency  of  the  others.     No  one  can  be  sure  of  the 
success  of  any  extensive  breeding  experiment,  but  this 
attempt  has  been  well  started  and  seems  to  present  no 
peculiar  difficulty.     Among  other  reasons  for  choosing 
moths  for  the  purpose,  is  that  they  are  born  adults,  not 
changing  in  stature  after  they  have  emerged  from  the 
chrysalis  and  shaken  out  their  wings.     Their  families 


VII.]  DISCUSSION  OF  THE  DATA  OF  STATURE.  137 

are  of  a  convenient  size  for  statistical  purposes,  say  from 
50  to  100,  neither  too  few  to  make  satisfactory  Schemes, 
nor  unmanageably  large.  They  can  be  mounted  as 
we  all  know,  after  their  death,  with  great  facility,  and 
be  remeasured  at  leisure.  An  intelligent  and  expe- 
rienced person  can  carry  on  a  large  breeding  establish- 
ment in  a  small  room,  supplemented  by  a  small  garden. 
The  methods  used  and  the  results  up  to  last  spring, 
have  been  described  by  Mr.  Merrifield  in  papers  read 
February  and  December  1887,  and  printed  in  the  Tran- 
sactions of  the  Entomological  Society.  I  speak  of  this 
now,  in  hopes  of  attracting  the  attention  of  some  who 
are  competent  and  willing  to  carry  on  collateral  experi- 
ments with  the  same  breed,  or  with  altogether  different 
species  of  moths. 


CHAPTER  VIII. 

DISCUSSION   OF   THE    DATA    OF   EYE    COLOUR. 

Preliminary  Remarks. — Data. — Persistence  of  Eye-Colour  in  tlie  Popula- 
tion.— Fundamental  Eye-Colours. — Principles  of  Calculation. — Results. 

Preliminary  Remarhs. — In  this  chapter  I  will  test 
the  conclusions  respecting  stature  by  an  examination 
into  hereditary  Eye-colour.  Supposing  all  female 
measures  to  have  been  transmuted  to  their  male  equi- 
valents, it  has  been  shown  (l)  that  the  possession  of 
each  unit  of  peculiarity  of  stature  in  a  man  [that  is  of 
each  unit  of  difference  from  the  average  of  his  race] 
when  the  man's  ancestry  is  unknown,  implies  the  exist- 
ence on  an  average  of  just  one- third  of  a  unit  of  that 
jDCculiarity  in  his  "Mid-Parent,"  and  consequently  of 
the  same  amount  in  each  of  his  parents ;  also  just  one- 
third  of  a  unit  in  his  Son ;  (2)  that  each  unit  of  pecu- 
liarity in  each  ancestor  taken  singly,  is  reduced  in 
transmission  according  to  the  following  average  scale  ; — 
a  Parent  transmits  only  |-,  and  a  Grand-Parent  only  -^^. 
Stature  and  Eye-colour  are  not  only  different  as 
qualities,  but  they  are  more  contrasted  in  hereditary 


CH.  VIII.]    DISCUSSION  OF  THE  DATA  OF  EYE  COLOUR.       139 

behaviour  than  perhaps  any  other  common  qualities. 
Parents  of  different  Statures  usually  transmit  a  blended 
heritage  to  their  children,  but  parents  of  different  Eye- 
colours  usually  transmit  an  alternative  heritage.  If  one 
parent  is  as  much  taller  than  the  average  of  his  or  her 
sex  as  the  other  parent  is  shorter,  the  Statures  of  their 
children  will  be  distributed,  as  we  have  already  seen,  in 
nearly  the  same  way  as  if  the  parents  had  both  been 
of  medium  height.  But  if  one  parent  has  a  light  Eye- 
colour  and  the  other  a  dark  Eye-colour,  some  of  the 
children  will,  as  a  rule,  be  light  and  the  rest  dark ;  they 
will  seldom  be  medium  eye-coloured,  like  the  children 
of  medium  eye-coloured  parents.  The  blending  in 
Stature  is  due  to  its  being  the  aggregate  of  the  quasi- 
independent  inheritances  of  many  separate  parts,  while 
Eye-colour  appears  to  be  much  less  various  in  its 
origin.  If  notwithstanding  this  two-fold  difference 
between  the  qualities  of  Stature  and  Eye-colour,  the 
shares  of  hereditary  contribution  from  the  various 
ancestors  are  alike  in  the  two  cases,  as  I  shall  show  that 
they  are,  we  may  with  some  confidence  expect  that  the 
law  by  which  those  hereditary  contributions  are  found 
to  be  governed,  may  be  widely,  and  perhaps  universally 
applicable. 

Data. — My  data  for  hereditary  Eye-colour  are  drawn 
from  the  same  collection  of  "Eecords  of  Family 
Faculties"  ("E.F.F.")  as  those  upon  which  the  inquiries 
into  hereditary  Stature  were  principally  based.  I  have 
analysed  the  general  value  of  these  data  in  respect  to 


140  NATURAL  INHERITANCK  [chap. 

Stature,  and  sliown  that  they  were  fairly  trustworthy. 
I  think  they  are  somewhat  more  accurate  in  respect  to 
Eye-colour,  upon  which  family  portraits  have  often 
furnished  direct  information,  while  indirect  information 
has  been  in  other  cases  obtained  from  locks  of  hair  that 
were  preserved  in  the  family  as  mementos. 

Persistence  of  Eye-colour  in  the  Population. — The 
first  subject  of  our  inquiry  must  be  into  the  existence  of 
any  slow  change  in  the  statistics  of  Eye-colour  in  the 
English  j)opulation,  or  rather  in  that  particular  part  of 
it  to  which  my  returns  apply,  that  ought  to  be  taken 
into  account  before  drawing  hereditary  conclusions. 
For  this  purpose  I  sorted  the  data,  not  according  to  the 
year  of  birth,  but  according  to  generations,  as  that 
method  best  accorded  with  the  particular  form  in  which 
all  my  E.F.F.  data  are  compiled.  Those  persons  who 
ranked  in  the  Family  Kecords  as  the  '^  children  '^  of  the 
pedigree,  were  counted  as  generation  I.  ;  their  parents, 
uncles  and  aunts,  as  generation  11.  ;  their  grandparents, 
great  uncles,  and  great  aunts,  as  generation  III. ;  their 
great  grandparents,  and  so  forth,  as  generation  IV.  No 
account  was  taken  of  the  year  of  birth  of  the  "  children," 
except  to  learn  their  age ;  consequently  there  is  much 
overlapping  of  dates  in  successive  generations.  We 
may  however  safely  say,  that  the  persons  in  generation 
I.  belong  to  quite  a  different  period  to  those  in  genera- 
tion III.,  and  the  persons  in  II.  to  those  in  IV.  I  had 
intended  to  exclude  all  children  under  the  age  of  eight 
years,  but  in  this  particular  branch  of  the  inquiry,  I 


viil]        discussion  OF  THE  DATA  OF  EYE  COLOUR.         141 

fear  tliat  some  cases  of  young  cliildren  have  been  acci- 
dentally included.  I  would  willingly  have  taken  a  later 
limit  than  eight  years,  but  could  not  spare  the  data 
that  would  in  that  case  have  been  lost  to  me. 

A  great  variety  of  terms  are  used  by  the  various 
compilers  of  the  "  Family  Kecords "  to  express  Eye- 
colours.  I  began  by  classifying  them  under  the  follow- 
ing eight  heads  ; — 1,  light  blue  ;  2,  blue,  dark  blue ; 
3,  grey,  blue-green ;  4,  dark  grey,  hazel ;  5,  light  brown ; 
6,  brown  ;  7,  dark  brown ;  8,  black.  Then  I  constructed 
Table  15.  • 

The  diagram,  page  143,  clearly  conveys  the  signifi- 
cance of  the  figures  in  Table  15.  Considering  that 
the  groups  into  which  the  observations  are  divided  are 
eiffht  in  number,  the  observations  are  far  from  beino; 
sufiiciently  numerous  to  justify  us  in  expecting  clean 
results ;  nevertheless  the  curves  come  out  surprisingly 
well,  and  in  accordance  with  one  another.  There  can 
be  little  doubt  that  the  change,  if  any,  during  four 
successive  generations  is  very  small,  and  much  smaller 
than  mere  memory  is  competent  to  take  note  o£  I 
therefore  disregard  a  current  popular  belief  in  the  exist- 
ence of  a  gradual  darkening  of  the  British  population, 
and  shall  treat  the  eye-colours  of  those  classes  of 
our  race  who  have  contributed  the  records,  as  having 
been  statistically  persistent  during  the  period  under 
discussion. 

The  concurrence  of  the  four  curves  for  the  four 
several  generations,  affords  internal  evidence  of  the 
trustworthiness   of  the  data.     For   supposing    we   had 


142  NATURAL  INHERITANCE.  [chap. 

curves  that  exactly  represented  the  true  Eye- colours  for 
the  four  generations,  they  would  either  be  concurrent 
or  they  would  not.  If  these  curves  were  concurrent, 
the  errors  in  the  R.F.F.  data  must  have  been  so 
curiously  distributed  as  to  preserve  the  concurrence. 
If  these  curves  were  not  concurrent,  then  the  errors 
in  the  E.F.F.  data  must  have  been  so  curiously  distri- 
buted as  to  neutralise  the  non- concurrence.  Both  of 
these  suppositions  are  improbable,  and  we  must  con- 
clude that  the  curves  really  agree,  and  that  the  R.F.F. 
errors  are  not  large  enough  to  spoil  the  agreement. 
The  close  similarity  of  the  two  curves,  derived  respec- 
tively from  the  whole  of  the  male  and  the  whole  of 
the  female  data,  and  the  more  perfect  form  of  the  curve 
derived  from  the  aggregate  of  all  the  cases,  are 
additional  evidences  in  favour  of  the  goodness  of  the 
data  on  the  whole. 

Fundamental  Eye-colours. — It  is  agreed  among  writers 
{cf.  A.  de  Candolle,  see  footnote  overleaf)  that  the  one 
important  division  of  eye-colours  is  into  the  light  and 
the  dark.  The  medium  tints  are  not  numerous,  but 
may  be  derived  from  any  one  of  four  distinct  origins. 
They  may  be  hereditary  with  no  notable  variation,  they 
may  be  varieties  of  light  parentage,  they  may  be 
varieties  of  dark  parentage,  or  they  may  be  blends. 
Medium  tints  are  classed  in  my  list  under  the  heading 
"4.  Dark  grey,  hazel;"  these  form  only  127  per 
cent,  of  all  the  observed  cases.  In  medium  tints,  the 
outer  portion  of  the  iris  is  often  of  a  dark  grey  colour, 


mi.]        DISCUSSION  OF  THE  DATA  OF  EYE  COLOUR.         143 

Percentages  of  the  Various  Eye-colours  in  Four  Successive  Generations. 


Number 

of 

cases 


,Q 

Sb 

.^ 

a 

0 

be 

g 

.0 

'd 

^ 

-a 

S 

aT 

^ 

•¥ 

1l 

% 

^ 

2 

^ 

to 

M 


O 


H 


913 


1515 


1477 


5S5 


2277 


2213 


Generation  IV, 


Total  Males 


,,     Females 


4490 


Total  cases 


IG  .16. 


144  NATURAL  INHERITANCE.  [cuap. 

and  the  inner  of  a  hazel.  The  proportion  between  the 
grey  and  the  hazel  varies  in  different  cases,  and  the 
eye-colour  is  then  described  as  dark  grey  or  as  hazel, 
according  to  the  colour  that  happens  most  to  arrest 
the  attention  of  the  observer.  For  brevity,  I  will 
henceforth  call  all  intermediate  tints  by  the  one  name 
of  hazel. 

I  will  now  investigate  the  history  of  those  hazel  eyes 
that  are  variations  from  light  or  from  dark  respectively, 
or  that  are  blends  between  them.  It  is  reasonable  to 
suppose  that  the  residue  which  were  inherited  from 
hazel-eyed  parents,  arose  in  them  or  in  their  prede- 
cessors either  as  variations  or  as  blends,  and  therefore 
the  result  of  the  investigation  will  enable  us  to  assort 
the  small  but  troublesome  group  of  hazel  eyes  in  an 
equitable  proportion  between  light  and  dark,  and  thus 
to   simplify  our  inquiry. 

The  family  records  include  168  families  of  brothers 
and  sisters,  counting  only  those  who  were  above  eight 
years  of  age,  in  whom  one  member  at  least  had  hazel 
eyes.  For  distinction  I  will  describe  these  as  "  hazel- 
eyed  families  ;  "  not  meaning  thereby  that  all  the 
children  have  that  peculiarity,  but  only  one  or  more  of 
them.  The  total  number  of  the  brothers  and  sisters 
in  the  168  hazel-eyed  families  is  948,  of  whom  302  or 
about  one-third  have  hazel  eyes.  The  eye-colours  of 
all  the  2  x  168,  or  336  parents,  are  given  in  the  records, 
but  only  those  of  449  of  the  grandparents,  whose 
number  would  be  672,  were  it  not  for  a  few  cases  of 
cousin  marriages.     Thus  I  have  information  concerning 


VIII.]        DISCUSSION  OF  THE  DATA  OF  EYE  COLOUR.  145 

about  only  two-tliirds  of  the  grandparents,  but  this 
will  suffice  for  our  purpose.  The  results  are  given  in 
Table  16. 

It  will  be  observed  that  the  distribution  of  eye-colour 
among  the  grandparents  of  the  hazel-eyed  families  is 
nearly  identical  with  that  among  the  population  at 
large.  But  among  the  parents  there  is  a  notable 
difference  ;  they  have  a  decidedly  larger  percentage 
of  light  eye-colour  and  a  slightly  smaller  proportion 
of  dark,  while  the  hazel  element  is  nearly  doubled. 
A  similar  change  is  superadded  in  the  children.  The 
total  result  in  passing  from  generations  III.  to  I.,  is  that 
the  percentage  of  the  light  eyes  is  diminished  from 
60  or  61  to  45,  therefore  by  one  quarter  of  its  original 
amount,  and  that  the  percentage  of  the  dark  eyes  is 
diminished  from  26  or  27  to  23,  that  is  by  about  one- 
eighth  of  its  original  amount,  the  hazel  element  in 
either  case  absorbiDg  the  difference.  It  follows  that 
the  chance  of  a  light-eyed  parent  having  hazel  off- 
spring, is  about  twice  as  great  as  that  of  a  dark-eyed 
parent.  Consequently,  since  hazel  is  twice  as  likely  to 
be  met  with  in  any  given  light-eyed  family  as  in  a 
given  dark- eyed  one,  we  may  look  upon  two-thirds  of 
the  hazel  eyes  as  being  fundamentally  light,  and  one- 
third  of  them  as  fundamentally  dark.  I  shall  allot 
them  rateably  in  that  proportion  between  light  and 
dark,  as  nearly  as  may  be  without  using  fractions,  and 
so   get  rid  of  them.      M.   Alphonse  de   CandoUe^  has 

1  Heredite  de  la  Conleur  des  Yeux  dans  I'Espece  humaine,"  par 
M.  Alphonse  de  Candolle.  "  Arch.  Sc.  Phys.  et  Nat.  Geneva,"  Aug.  1884, 
3rd  period,  vol.  xii.  p.  97. 


146  NATURAL  INHERITANCE.  [chap. 

also  shown  from  liis  data,  that  yeux  gris  (which  I  take 
to  be  the  equivalent  of  my  hazel)  are  referable  to  a 
light  ancestry  rather  than  to  a  dark  one,  but  his  data 
are  numerically  insufficient  to  warrant  a  precise  estimate 
of  the  relative  frequency  of  their  derivation  from  each 
of  these  two  sources. 

In  the  following   discussion   I   shall  deal  only  with 
those  fraternities  in  which  the  Eye-colours   are  known 
of  the  two    Parents  and    of   the    four    Grand- Parents. 
There  are  altogether    211    of   such  groups,   containing 
an  aggregate  of  1023  children.      They  do  not,  however, 
belong  to    211    different    family    stocks,    because   each 
stock  which  is  complete  up  to  the  great  grand-parents 
inclusive    (and  I  have    fourteen    of  these)    is    capable 
of  yielding  three  such  groups.     Thus,  group  1  contains 
a,    the   ^'  children ; "     h,    the    parents ;     c,    the    grand- 
parents.     Group    2    contains    a,     the    father   of    the 
"  children "  and  his    brothers    and  his    sisters ;  h,   the 
parents    of   the    father ;    c,    the    grand-parents    of   the 
father.     Group  3  contains  the  corresponding  selections 
on  the  mother's  side.      Other  family  stocks  furnish  two 
groups.     Gufc  of  these  and  other  data.  Tables   19  and 
20  have    been    made.      In   Table    19    I   have  grouped 
the  families  together  whose  two  parents  and  four  grand- 
parents  present   the  same    combination  of  Eye-colour, 
no  group,   however,  being  accepted  that  contains   less 
than  twenty  children.     The   data  in  this   table  enable 
us  to  test  the  average  correctness  of  the  law  I  desire 
to   verify,    because    many  persons    and   many  families 
appear  in  the  same  grouj),  and  individual  peculiarities 


viil]        discussion  OF  THE  DATA  OF  EYE  COLOUR.  147 

tend  to  neutralise  each  other.  In  Table  20  I  have 
separately  classified  on  the  same  system  all  the  families, 
78  in  number,  that  consist  of  six  or  more  children. 
These  data  enable  us  to  test  the  trustworthiness  of  the 
law  as  applied  to  individual  families.  It  will  be 
seen  from  my  way  of  discussing  them,  that  smaller 
fraternities  than  these  could  not  be  advantageously 
dealt  with. 

It  will  be  noticed  that  I  have  not  printed  the  number 
of  dark- eyed  children  in  either  of  these  tables.  They 
are  implicitly  given,  and  are  instantly  to  be  found  by 
subtracting  the  number  of  light-eyed  children  from 
the  total  number  of  children.  Nothing  would  have 
been  gained  by  their  insertion,  while  compactness  would 
have  been  sacrificed. 

The  entries  in  the  tables  are  classified,  as  I  said, 
according  to  the  various  combinations  of  light,  hazel, 
and  dark  Eye-colours  in  the  Parents  and  Grand-Parents. 
There  are  six  different  possible  combinations  among  the 
two  Parents,  and  15  among  the  four  Grand-Parents, 
making  6  x  15,  or  90  possible  combinations  altogether. 
The  number  of  observations  are  of  course  by  no  means 
evenly  distributed  among  the  classes.  I  have  no  returns 
at  all  under  more  than  half  of  them,  while  the  entries 
of  two  light-eyed  Parents  and  four  light-eyed  Grand- 
Parents  are  proportionately  very  numerous. 

The  question  of  marriage  selection  in  respect  to 
Eye-colour,  has  been  already  discussed  briefly  in  p.  86. 
It  is  a  less  simple  statistical  question  than  at  a  first  sight 
it  may  appear  to  be.  so  I  will  not  discuss  it  farther. 

L  2 


148  NATURAL  INHERITANCE.  [chap. 

Principles  of  Calculation. — I  have  next  to  show 
how  the  expectation  of  Eye-colour  among  the  children 
of  a  given  family  is  to  be  reckoned  on  the  basis  of 
the  same  law  that  held  in  respect  to  stature,  so  that 
calculations  of  the  probable  distribution  of  Eye-colours 
may  be  made.  They  are  those  that  fill  the  three  last 
columns  of  Tables  19  and  20,  which  are  headed  I., 
IL,  and  III.,  and  are  placed  in  juxtaposition  with 
the  observed  facts  entered  in  the  column  hea.ded 
"  Observed."  These  three  columns  contain  calculations 
based  on  data  limited  in  three  difi'erent  ways,  in  order 
the  more  thoroughly  to  test  the  applicability  of  the 
law  that  it  is  desired  to  verify.  Column  I.  contains 
calculations  based  on  a  knowledge  of  the  Eye-colours 
of  the  Parents  only  ;  II.  contains  those  based  on  a 
knowledge  of  those  of  the  Grand-Parents  only ; 
III.  contains  those  based  on  a  knowledge  of  those 
both  of  the  Parents  and  of  the  Grand-Parents,  and 
of  them  only. 

I.  Eye-colours  given  of  the  two  Parents — 

Let  the  letter  S  be  used  as  a  symbol  to  signify  the 
subject  (or  person)  for  whom  the  expected  heritage  is  to 
be  calculated.  Let  F  stand  for  the  words  "  a  parent  of 
S ; "  Gi  for  "  a  grandparent  of  S ; "  Go  for  "a  great- 
grandparent  of  S,"  and  so  on. 

We  must  begin  by  stating  the  problem  as  it  would 
stand  if  Stature  was  under  consideration,  and  then 
modify  it  so  as  to  apply  to  Eye-colour.  Suppose  then, 
that  the  amount  of  the  peculiarity  of  Stature  j)os- 
sesscd  by  F  is  equal  to  D,  and  that  nothing  whatever 


VIII.]        DISCUSSION  OF  THE  DATA  OF  EYE  COLOUR.         149 

is  known  with  certainty  of  any  of  tlie  ancestors  of 
S  except  F.  We  have  seen  that  though  nothing  may 
actually  be  known,  yet  that  something  definite  is  implied 
about  the  ancestors  of  F,  namely,  that  each  of  his  two 
parents  (who  will  stand  in  the  order  of  relationship 
of  Gi  to  S)  will  on  the  average  possess  J^D.  Similarly 
that  each  of  the  four  grandparents  of  F  (who  will  stand 
in  the  order  of  G2  to  S)  will  on  the  average  possess 
^D,  and  so  on.  Again  we  have  seen  that  F,  on  the 
average,  transmits  to  S  only  J  of  his  peculiarity ,-  that 
Gi  transmits  only  ^^ ;  G2  only^^^,  and  so  on.  Hence 
the  aggregate  of  the  heritages  that  may  be  expected 
to  converge  through  F  upon  S,  is  contained  in  the 
following  series  : — 

That  is  to  say,  each  parent  must  in  this  case  be 
considered  as  contributino;  0"30  to  the  heritasre  of  the 
child,  or  the  two  parents  together  as  contributing  0*60, 
leaving  an  indeterminate  residue  of  0*40  due  to  the 
influence  of  ancestry  about  whom  nothing  is  either 
known  or  implied,  except  that  they  may  be  taken  as 
members  of  the  same  race  as  S. 

In  applying  this  problem  to  Eye-colour,  we  must  bear 
in  mind  that  the  fractional  chance  that  each  member 
of  a  family  will  inherit  either  a  light  or  a  dark  Eye- 
colour,  must  be  taken  to  mean  that  that  same  fraction 


150  NATURAL  INHERITANCE.  [chap. 

of  tlie  total  number  of  cliilclren  in  the  family  will 
probably  possess  it.  Also,  as  a  consequence  of  this 
view  of  the  meaning  of  a  fractional  chance,  it  follows 
that  the  residue  of  0*40  must  be  rateably  assigned 
between  light  and  dark  Eye-colour,  in  the  proportion 
in  which  those  Eye-colours  are  found  in  the  race 
generally,  and  this  was  seen  to  be  (see  Table  16)  as 
61*2  :26'1  ;  so  I  allot  0*28  out  of  the  above  residue 
of  0'40  to  the  heritage  of  light,  and  0"12  to  the  heritage 
of  dark.  When  the  parent  is  hazel-eyed  I  allot  f  of 
his  total  contribution  of  0'30,  i.e.,  0*20  to  light,  and 
■J-,  i.e.  O'lO  to  dark.  These  chances  are  entered  in  the 
first  pair  of  columns  headed  I.  in  Table  17. 

The  pair  of  columns  headed  I.  in  Table  18  shows 
the  way  of  summing  the  chances  that  are  given  in  the 
columns  that  have  a  similar  heading  in  Table  17.  By 
the  method  there  shown,  I  calculated  all  the  entries 
that  appear  in  the  columns  with  the  heading  I.  in  Tables 
19  and  20. 

II.  Eye-colours  given  of  the  four  Grand  Parents — 
Suppose  D  to  be  possessed  by  Gi  and  that  nothing 
whatever  is  known  with  certainty  of  any  other  ancestor 
of  S.  Then  it  has  been  shown  that  the  child  of  Gj 
(that  is  F)  will  possess  ^D  ;  that  each  of  the  two  parents 
of  Gi  (who  stand  in  the  relation  of  G2  to  S)  will  also 
possess  -|-D  ;  that  each  of  the  four  grandparents  of  Gi 
(who  stand  in  the  relation  of  G3  to  S)  will  possess  -^D, 
and  so  on.  Also  it  has  been  shown  that  the  shares 
of  their  several  peculiarities  that  will  on  the  average 
be  transmitted  by  F,  Gj,   Go,  &c.,  are  \,  y\j-,  ^i^,  &c., 


VIII.]         DISCUSSION  OF  THE  DATA  OF  EYE  COLOUR.  151 

respectively.  Hence  tlie  aggregate  of  the  probable 
heritages  from  Gi  are  expressed  by  the  following 
series  : — 

d/1x  -+1  xi+lx  2  x3^-+-x  4  xi+&c.    ] 

il2     V2*     3x2^      3^x26  Jl  Vl2     40 


So  that  each  grandparent  contributes  on  the  average 
0*16  (more  exactly  0'1583)  of  his  peculiarity  to  the 
heritage  of  S,  and  the  four  grandparents  contribute 
between  them  0*64,  leaving  36  indeterminate,  which 
when  rateably  assigned  gives  0"25  to  light  and  0*11 
to  dark.  A  hazel-eyed  grandparent  contributes,  accord- 
ing to  the  ratio  described  in  the  last  paragraph, 
0*10  to  light  and  0*06  to  dark.  All  this  is  clearly 
expressed  and  employed  in  the  columns  IL  of  Tables  17 
and  18. 

III.  Eye- colours  given  of  the  two  Parents  and  four 
Grand-Parents — 

Suppose  F  to  possess  D,  then  F  taken  alone.,  and  not 
in  connection  with  what  his  possession  of  D  might  imply 
concerning  the  contributions  of  the  previous  ancestry, 
will  contribute  an  average  of  0*25  to  the  heritage  of 
S.  Suppose  Gi  also  to  possess  D,  then  his  contribution 
together  with  what  his  possession  of  D  may  imply 
concerning  the  previous  ancestry,  was  calculated  in  the 
last  paragraph  as  D  x  ^^^  =D  x  0'075.  For  the  con- 
venience of  using  round  numbers  I  take  this  as 
DxO"08.      So    the    two    parents    contribute    between 


152  NATURAL  INHERITANCE.  [chap. 

them  0'50  of  the  peculiarity  of  S,  the  four  grand- 
parents together  with  what  they  imply  of  the  previous 
ancestry  contribute  0*32,  being  an  aggregate  of  0*82, 
leaving  a  residue  of  0"18  to  be  rateably  assigned  as 
0'12  to  light,  and  0'6  to  dark.  A  hazel-eyed  Parent 
is  here  reckoned  as  contributing  0'16  to  light  and  0*9  to 
dark;  a  hazel-eyed  Grand-Parent  as  contributing  0*5 
to  light  and  0*3  to  dark.  All  this  is  tabulated  in 
Table  17,  and  its  working  exjDlained  by  an  example  in 
the  columns  headed  III.  of  Table  1 8. 

Results. — A  mere  glance  at  Tables  19  and  20  will 
show  how  surprisingly  accurate  the  predictions  are,  and 
therefore  how  true  the  basis  of  the  calculations  must  be. 
Their  average  correctness  is  shown  best  by  the  totals 
in  Table  19,  which  give  an  aggregate  of  calculated 
numbers  of  light-eyed  children  under  Groups  I.,  II.,  and 
III.  as  623,  601,  and  614  respectively,  when  the  observed 
numbers  were  629  ;  that  is  to  say,  they  are  correct  in 
the  ratios  of  99,  96,  and  98  to  100. 

Their  trustworthiness  when  applied  to  individual 
families  is  shown  as  strongly  in  Table  20  whose  results 
are  conveniently  summarised  in  Table  21.  I  have  there 
classified  the  amounts  of  error  in  the  several  calculations  : 
thus  if  the  estimate  in  any  one  family  was  3  light- 
eyed  children,  and  the  observed  number  was  4,  I  should 
count  the  error  as  1  '0.  I  have  worked  to  one  place  of 
decimals  in  this  table,  in  order  to  bring  out  the  different 
shades  of  trustworthiness  in  the  three  sets  of  calcula- 
tions, which  thus    become  very  apparent.      It  will  be 


VIII.]        DISCUSSION  OF  THE  DATA  OF  EYE  COLOUR.  153 

seen  that  the  calculations  in  Class  III.  are  by  far  the 
most  precise.  In  more  than  one-half  of  those  calcula- 
tions the  error  does  not  exceed  0 "5,  whereas  in  more  than 
three -quarters  of  those  in  I.  and  II.  the  error  is  at  least  of 
that  amount.  Only  one-quarter  of  Class  III.,  but  some- 
where about  the  half  of  Classes  I.  and  II.,  are  more  than 
1*1  in  error.  In  comparing  I.  with  11. ,  we  find  I.  to 
be  slightly  but  I  think  distinctly  the  superior  estimate. 
The  relative  accuracy  of  III.  as  compared  with  I.  and 
II.,  is  what  we  should  have  expected,  supposing  the 
basis  of  the  calculations  to  be  true,  because  the  addi- 
tional knowledge  utilised  in  III.,  over  what  is  turned 
to  account  in  I.  and  II.,  must  be  an  advantage. 

My  returns  are  insufficiently  numerous  and  too 
subject  to  uncertainty  of  observation,  to  make  it  worth 
while  to  submit  them  to  a  moi*e  rigorous  analysis,  but 
the  broad  conclusion  to  which  the  present  results 
irresistibly  lead,  is  that  the  same  peculiar  hereditary 
relation  that  was  shown  to  subsist  between  a  man  and 
each  of  his  ancestors  in  respect  to  the  quality  of 
Stature,  also  subsists  in  respect  to  that  of  Eye-colour. 


CHAPTER  IX 


THE   ARTISTIC   FACULTY. 


Data. — Sexual  Distribution. — Marriage   Selection. — Regression. — Effect  of 

Bias  in  Marriage. 

Data. — It  is  many  years  since  I  described  the  family 
history  of  the  great  Painters  and  Musicians  in  Here- 
ditary  Genius.  The  inheritance  of  much  less  excep- 
tional gifts  of  Artistic  Faculty  will  be  discussed  in  this 
chapter,  and  from  an  entirely  different  class  of  data. 
They  are  the  answers  in  my  R.F.F  collection,  to  the 
question  of  ^'  Favourite  pursuits  and  interests  ?  Artistic 
aptitudes  ?  " 

The  list  of  persons  who  were  signalised  as  being 
especially  fond  of  music  and  drawing,  no  doubt 
includes  many  who  are  artistic  in  a  very  moderate 
degree.  Still  they  form  a  fairly  well  defined  class, 
and  one  that  is  easy  to  discuss  because  their  family 
history  is  complete.  In  this  respect,  they  are  much 
more  suitable  subjects  for  statistical  inquiry  than  the 
great  Painters  and  Musicians,  whose  biographers  usually 
say  little  or  nothing  of  their  non-artistic  relatives. 


CHAP.  IX.]  THE  ARTISTIC  FACULTY.  155 

The  object  of  the  present  chapter  is  not  to  give  a 
reply  to  the  simple  question,  whether  or  no  the  Artistic 
faculty  tends  to  be  inherited.  A  man  must  be  very 
crotchety  or  very  ignorant,  who  nowadays  seriously 
doubts  the  inheritance  either  of  this  or  of  any  other 
faculty.  The  question  is  whether  or  no  its  inheritance 
follows  a  similar  law  to  that  which  has  been  shown  to 
govern  Stature  and  Eye- colour,  and  which  has  been 
worked  out  with  some  completeness  in  the  foregoing 
chapters.  Before  answering  this  question,  it  will  be 
convenient  to  compare  the  distribution  of  the  Artistic 
faculty  in  the  two  sexes,  and  to  learn  the  influence 
it  may  exercise  on  marriage  selection. 

I  begcin   by  dividing  my  data   into  four   classes    of 
aptitudes  ;    the  first  was  for  music  alone  ;    the  second 
for   drawing   alone  ;    the    third   for    both    music    and 
drawing  ;  and  the  fourth  includes  all  those  about  whose 
artistic  capacities  a  discreet  silence  was  observed.     After 
prefatory   trials,    I    found   it    so    difficult    to    separate 
aptitude  for    music  from  aptitude  for  drawing,  that    I 
determined  to   throw  the  three  first   classes   into   the 
single  group  of  Artistic.    This  and  the  group  of  the  Non- 
Artistic  are  the  only  two  divisions  now  to  be  considered. 
A  difficulty  presented  itself  at  the  outset  in  respect 
to   the  families   that  included  boys,   girls,    and   young 
children,  whose  artistic  tastes  and  capacities  can  seldom 
be  fairly  judged,  while  they  are  liable  to  be  appraised 
too  favourably  by  the  compiler  of  the  Family  records, 
especially  if  he  or  she  was  one  of  their  parents.     As  the 
practice  of  picking  and  choosing  is  very  hazardous  in 


156  NATURAL  INHERITANCE.  [chap. 

statistical  inquiries,  however  fair  our  intentions  may  be, 
and  as  it  in  justice  always  excites  suspicion,  I  decided, 
though  with  much  regret  at  their  loss,  to  omit  the  wdiole 
of  those  who  were  not  adult. 

Sexual  Distribution. — Men  and  women,  as  classes, 
may  differ  little  in  their  natural  artistic  capacity, 
but  such  difference  as  there  is  in  adult  life  is  some- 
what in  favour  of  the  women.  Table  9b  contains 
894  cases,  447  of  men  and  447  of  women,  divided 
into  three  groups  according  to  the  rank  they  hold  in 
the  pedigrees.  These  groups  agree  fairly  well  among 
themselves,  and  therefore  their  aggregate  results  may 
be  freely  accepted  as  trustworthy.  They  sho^v  that 
28  per  cent,  of  the  males  are  Artistic  and  72  are 
Not  Artistic,  and  that  there  are  33  per  cent.  Artistic 
females  to  67  who  are  Not  Artistic.  Part  of  this 
female  superiority  is  doubtless  to  be  ascribed  to  the 
large  share  that  music  and  drawing  occupy  in  the 
education  of  w^omen,  and  to  the  greater  leisure  that 
most  girls  have,  or  take,  for  amusing  themselves.  If 
the  artistic  gifts  of  men  and  women  are  naturally  the 
same,  as  the  experience  of  schools  where  music  and 
drawing  are  taught,  apparently  shows  it  to  be,  the 
small  difference  observed  in  favour  of  women  in  adult 
life  would  be  a  measure  of  the  smallness  of  the  effect 
of  education  compared  to  that  of  natural  talent.  Dis- 
regarding the  distinction  of  sex,  the  figures  in  Table 
9b  show  that  the  number  of  Artistic  to  Non-Artistic 
persons  in  the  general  population  is  in  the  proportion 


IX.]  THE  ARTISTIC  FACULTY.  157 

of  30|  to  69^.  The  data  used  in  Table  22  refer  to  a 
considerably  larger  number  of  persons,  and  do  not 
include  more  tban  two-thirds  of  those  employed  in 
Table  9b,  and  they  make  the  proportion  to  be  31  to 
69.  So  we  shall  be  quite  correct  enough  if  we  reckon 
that  out  of  ten  persons  in  the  families  of  my  E.F.F. 
correspondents,  three  on  the  average  are  artistic  and 
seven  are  not. 

Marriage  Selection. — Table  9  b  enables  us  to  ascer- 
tain whether  there  is  any  tendency,  or  any  disinclination 
among  the  Artistic  and  the  Non- Artistic,  to  marry  within 
their  respective  castes.  It  shows  the  observed  fre- 
quency of  their  marriages  in  each  of  the  three  possible 
combinations ;  namely,  both  husband  and  wife  artistic  ; 
one  artistic  and  one  not ;  and  both  not  artistic.  The 
Table  also  gives  the  calculated  frequency  of  the  three 
classes,  supposing  the  pairings  to  be  regulated  by  the 
laws  of  chance.  There  is  I  think  trustworthy  evidence 
of  the  existence  of  some  slight  disinclination  to  marry 
within  the  same  caste,  for  signs  of  it  appear  in  each 
of  the  three  sets  of  families  with  which  the  Table 
deals.  The  total  result  is  that  there  are  only  36  per 
cent,  of  such  marriages  observed,  whereas  if  there  had 
been  no  disinclination  but  perfect  indifference,  the 
number  would  have  been  raised  to  42.  The  difference 
is  small  and  the  figures  are  few,  but  for  the  above 
reasons  it  is  not  likely  to  be  fallacious.  I  believe  the 
facts  to  be,  that  highly  artistic  people  keep  pretty  much 
to   themselves,  but  that  the  very  much  larger  body  of 


158  NATURAL  INHERITANCE.  [chap. 

moderately  artistic  people  do  not.  A  man  of  liiglily 
artistic  temperament  must  look  on  those  who  are 
deficient  in  it,  as  barbarians ;  he  would  continually 
crave  for  a  sj^mpathy  and  response  that  such  persons 
are  incapable  of  giving.  On  the  other  hand,  every 
quiet  unmusical  man  must  shrink  a  little  from  the  idea 
of  wedding  himself  to  a  grand  piano  in  constant  action, 
with  its  vocal  and  peculiar  social  accompaniments  ;  but 
he  might  anticipate  great  pleasure  in  having  a  wife  of 
a  moderately  artistic  temperament,  who  would  give 
colour  and  variety  to  his  prosaic  life.  On  the  other 
hand,  a  sensitive  and  imaginative  wife  would  be  con- 
scious of  needing  the  aid  of  a  husband  who  had  enough 
plain  common- sense  to  restrain  her  too  enthusiastic 
and  frequently  foolish  projects.  If  wife  is  read  for 
husband,  and  husband  for  wife,  the  same  argument 
still  holds  true. 

Eegression. — Having  disposed  of  these  preliminaries, 
we  will  now  examine  into  the  conditions  of  the  inherit- 
ance of  the  Artistic  Faculty.  The  data  that  bear  upon 
it  are  summarised  in  Table  22,  where  I  have  not  cared 
to  separate  the  sexes,  as  my  data  are  not  immerous 
enough  to  allow  of  more  subdivision  than  can  be 
helped.  Also,  because  from  such  calculations  as  I  have 
made,  the  hereditary  influences  of  the  two  sexes  in 
respect  to  art  appear  to  be  pretty  equal  :  as  they  are 
in  respect  to  nearly  every  other  characteristic,  exclu- 
sive of  diseases,   that  I  have  examined. 

It  is  perfectly  conceivable  that  the  Artistic  Faculty 


IX.]  THE  ARTISTIC  FACULTY.  159 

in  any  person  might  be  somehow  measured,  and  its 
amount  determined,  just  as  we  may  measure  Strength, 
the  power  of  Discrimination  of  Tints,  or  the  tenacity  of 
Memory.  Let  us  then  suppose  the  measurement  of  the 
Artistic  Faculty  to  be  feasible  and  to  have  been  often 
performed,  and  that  the  measures  of  a  large  number 
of  persons  were  thrown  into  a  Scheme. 

It  is  reasonable  to  expect  that  the  Scheme  of  the 
Artistic  Faculty  would  be  approximately  Normal  in 
its  proportions,  like  those  of  the  various  Qualities  and 
Faculties  whose  measures  were  given  in  Tables  2  and  3. 

It  is  also  reasonable  to  expect  that  the  same  law  of 
inheritance  might  hold  good  in  the  Artistic  Faculty 
that  was  found  to  hold  good  both  in  Stature  and  in 
Eye  colour ;  in  other  words,  that  the  value  of  Filial 
Kegression  would  in  this  case  also  be  f. 

We  have  now  to  discover  whether  these  assumptions 
are  true  without  any  help  from  direct  measurement. 
The  problem  to  be  solved  is  a  pretty  one,  and  will 
illustrate  the  method  by  which  many  problems  of  a 
similar  class  have  to   be  worked. 

Let  the  graduations  of  the  scale  by  which  the 
Artistic  Faculty  is  supposed  to  be  measured,  be  such 
that  the  unit  of  the  scale  shall  be  equal  to  the  Q  of 
the  Art- Scheme  of  the  general  population.  Call  the 
unknown  M  of  the  Art-Scheme  of  the  population,  P. 
Then,  as  explained  in  page  52,  the  measure  of  any 
individual  will  be  of  the  form  P  -f  (zb  D),  where  D 
is  the  deviation  from  P.  The  first  fact  we  have  to 
deal  with  is,  that  only  30  per  cent,  of  the  population 


IGO  NATURAL  INHERITANCE.  [chap. 

are  Artistic.  Therefore  no  person  whose  Grade  in  the 
Art-Scheme  does  not  exceed  70°  can  be  reckoned  as 
Artistic.  Referring  to  Table  8  we  see  that  the  value 
of  D  for  the  Grade  of  70°  is  +  0*78  ;  consequently  the 
art-measure  of  an  Artistic  person,  when  reckoned  in 
units  of  the  accepted  scale,  must  exceed  P-}-0*78. 

The  average  art-measure  of  all  persons  whose  Grade 
is  higher  than  70°,  may  be  obtained  with  sufficient 
ajDproximation  by  taking  the  average  of  all  the  values 
given  in  Table  8,  for  every  Grade,  or  more  simply 
for  every  odd  Grade  from  71°  to  99°  inclusive.  It 
will  be  found  to  be  l*7l.  Therefore  an  artistic 
person  has,  on  the  average,  an  art-measure  of 
P  -h  l'7l.  We  will  consider  persons  of  this  measure 
to  be  representatives  of  the  whole  of  the  artistic  por- 
tion of  the  Population.  It  is  not  strictly  correct  to 
do  so,  but  for  approximative  purposes  this  rough  and 
ready  method  will  suffice,  instead  of  the  tedious  process 
of  making  a  separate  calculation  for  each  Grade. 

The  IVI  of  the  Co -Fraternity  born  of  a  group  of 
Mid-Parents  whose  measure  is  P  -h  171  will  be 
P  -1-  (f  X  1-71)  or  (P  +  1-4).  We  will  call  this  value 
C.  The  Q  of  this  or  any  other  Co-Fraternity  may  be 
expected  to  bear  approximately  the  same  ratio  to  the 
Q  of  the  general  population,  that  it  did  in  the  case 
of  Stature,  namely,  that  of  1'5  to  17.  Therefore  the 
Q  of  the  Co-Fraternity  who  are  born  of  Mid-Parents 
whose  Art-measure  is  C,  will  be  0'88. 

The  artistic  members  of  this  Co-Fraternity  will  be  those 
whose  measures  exceed  (P  -h  078}.     We  may  write  this 


IX.]  THE  ARTISTIC  FACULTY.  161 

value  in  the  form  of  {(P  +  1-4) -0-36},  or  {C  —  0-36}. 
Table  8  shows  that  the  Deviation  of— 0'36  is  found 
at  the  Grade  of  40°.  Consequently  40  per  cent,  of 
this  Co-Fraternity  will  be  Non- Artistic  and  60  per  cent, 
will  be  Artistic.  Observation  Table  23  shows  the 
numbers  to  be  36  and  64,  wdiich  is  a  very  happy 
agreement. 

Next  as  regards  the  Non-Artistic  Parents.  The  Non- 
Artistic  portion  of  the  Population  occupy  the  70  first 
Grades  in  the  Art-Scheme,  and  may  be  divided  into 
two  groups ;  one  consisting  of  40  Grades,  and  standing 
between  the  Grades  of  70°  and  30°,  or  between  the 
Grade  of  50°  and  20  Grades  on  either  side  of  it,  the 
average  Art-measure  of  whom  is  P ;  the  other  group 
standing  below  30°,  whose  average  measure  maybe  taken 
to  be  P  —  1*71,  for  the  same  reason  that  the  group 
above  70°  was  taken  as  P  +  1'71.  Consequently  the 
average  measure  of  the  entire  Non-Artistic  class  is 
-J^{(40  X  P)  -h  30  (P  -  1-71)} 
=3  P  -  f g  X  1-71  =  P  -  073. 
Supposing  Mid-Parents  of  this  measure,  to  represent  the 
entire  Non- Artistic  group,  their  offspring  will  be  a  Co- 
Fraternity  having  for  their  IVI  the  value  of  P  — {f  x  0*73} 
or  P  —  0*49,  which  we  will  call  C,  and  for  their  Q  the 
value  of  0'88  as  before. 

Such  among  them  as  exceed  {P  —  0'78},  which  we 
may  write  in  the  form  of  {(P  —  0*49)  +  (1'27)},  or 
{C  +  1*27},  are  Artistic,  and  they  are  those  who, 
according  to  Table  8,  rank  higher  than  the  Grade  83°. 
In  other  words,   83   per  cent,  of  the  children  of  Non- 

M 


162  NATURAL  INHERITANCE.  [chap. 

Artistic  parents  will  be  Non-Artistic,  and  tlie  re- 
mainder of  17  per  cent,  will  be  Artistic.  Observation 
gives  the  values  of  79  and  21,  wbicb  is  a  very  fair 
coincidence. 

When  one  parent  is  Artistic  and  the  other  Not,  their 
joint  hereditary  influence  would  be  the  average  of  the 
above  two  cases;  that  is  to  say,  -^  (40  4-  83),  or  61-^ 
per  cent,  of  their  children  would  be  Non -Artistic,  and 
^  (60  ■+  17),  or  381  would  be  Artistic.  The  observed 
numbers  are  61  and  39,  which  agree  excellently  well. 

We  may  therefore  conclude  that  the  same  law  of 
Eegression,  and  all  that  depends  upon  it,  which  governs 
the  inheritance  both  of  Stature  and  Eye-colour,  applies 
equally  to  the  Artistic  Faculty. 

Effect  of  Bias  in  Marriage. — The  slight  apparent 
disinclination  of  the  Artistic  and  the  Non- Artistic  to 
marry  in  their  own  caste,  is  hardly  worth  regarding, 
but  it  is  right  to  clearly  understand  the  extreme  effect 
that  might  be  occasioned  by  Bias  in  Marriage.  Suppose 
the  attraction  of  like  to  like  to  become  paramount,  so 
that  each  individual  in  a  Scheme  married  his  or  her 
nearest  available  neighbour,  then  the  Scheme  of  Mid- 
Parents  would  be  practically  identical  wi  th  the  Scheme 
drawn  from  the  individual  members  of  the  population. 
In  the  case  of  Stature  their  Q  would  be  1'7  inch,  instead 
of  1'7  divided  by  \/2.  The  regression  and  subsequcut 
dispersion  remaining  unchanged,  the  Q  of  the  offspring 
would  consequently  be  increased. 

On  the  other  hand,  suppose  the  attraction  of  contrast 


IX.]  THE  ARTISTIC  FACULTY.  163 

to  become  suddenly  paramount,  so  that  Grade  99° 
paired  in  an  instant  witli  Grade  1°;  next  98°  with  2°; 
and  so  on  in  order,  until  the  languid  desires  of  49°  and 
51°  were  satisfied  last  of  all.  Then  every  one  of 
the  Mid-Parents  would  be  of  precisely  the  same  stature 
P.  Consequently  their  Q  would  be  zero  ;  and  that  of 
the  system  of  the  Mid-Co-Fraternities  would  be  zero 
also  ;  hence  the  Q  of  the  next  generation  would  con- 
tract to  the  Q  of  a  Co-Fraternity,  that  is  to  1'5  inch. 

Whatever  might  be  the  character  or  strength  of  the 
bias  in  marriage  selection,  so  long  as  it  remains  constant 
the  Q  of  the  population  would  tend  to  become  con- 
stant also,  and  the  statistical  resemblance  between 
successive  generations  of  the  future  Population  would 
be  ensured.  The  stability  of  the  balance  between  the 
opposed  tendencies  of  Eegression  and  of  Co-Fraternal 
expansion  is  due  to  the  Eegression  increasing  with  the 
Deviation.  Its  efi'ect  is  like  that  of  a  spring  acting 
against  a  weight ;  the  spring  stretches  until  its  gradually 
increasing  resilient  force  balances  the  steady  pull  of  the 
weight,  then  the  two  forces  of  spring  and  weight  are 
in  stable  equilibrium.  For,  if  the  weight  be  lifted  by  the 
hand,  it  will  obviously  fall  down  again  as  soon  as  the 
hand  is  withdrawn ;  or  again,  if  it  be  depressed  by  the 
hand,  the  resilience  of  the  spring  will  become  increased, 
and  the  weight  will  rise  up  again  when  it  is  left  free  to 
do  so. 


M  2 


CHAPTEE   X. 


13ISEASE. 


Preliminary  Problem. — Data. — Trustwortliiiiess  of  R.F.F.  Data. — Mixture 
of  Inheritance?. — Consumption  :  General  Remai-ks  ;  Parent  to  Child  ; 
Distribution  of  Praternities ;  Severely  Tainted  Fraternities ;  Con- 
snmptivity. — Data  for  Hereditary  Diseases. 

The  vital  statistics  of  a  population  are  tliose  of  a 
vast  army  marching  rank  behind  rank,  across  the 
treacherous  table-lancl  of  life.  Some  of  its  members 
drop  out  of  sight  at  every  step,  and  a  new  rank  is  ever 
rising  up  to  take  the  place  vacated  by  the  rank  that 
preceded  it,  and  which  has  already  moved  on.  The  popu- 
lation retains  its  peculiarities  although  the  elements  of 
which  it  is  composed  are  never  stationary,  neither  are 
the  same  individuals  present  at  any  two  successive 
epochs.  In  these  respects,  a  population  may  be  com- 
pared to  a  cloud  that  seems  to  rejDOse  in  calm  upon  a 
mountain  plateau,  while  a  gale  of  wind  is  blowing 
over  it.  The  outline  of  the  cloud  remains  unchanged, 
although  its  elements  are  in  violent  movement  and  in 
a  condition  of  perpetual  destruction  and  renewal.     Tlie 


X.]  DISEASE.  1G5 

well  understood  cause  of  sucli  clouds  is  the  deflection 
of  a  wind  laden  with  invisible  vapour,  by  means  of 
the  sloping  flanks  of  the  mountain,  up  to  a  level  at 
which  the  atmosphere  is  much  colder  and  rarer  than 
below.  Part  of  the  invisible  vapour  with  wdiich  the 
wdnd  was  charged,  becomes  thereby  condensed  into  the 
minute  particles  of  water  of  which  clouds  are  formed. 
After  a  while  the  process  is  reversed.  The  particles 
of  cloud  having  been  carried  by  the  wind  across  the 
plateau,  are  swept  down  the  other  side  of  it  again  to  a 
lower  level,  and  during  their  descent  they  return  into 
invisible  vapour.  Both  in  the  cloud  and  in  the 
population,  there  is  on  the  one  hand  a  continual  supply 
and  inrush  of  new  individuals  from  the  unseen ;  they 
remain  a  while  as  visible  objects,  and  then  disappear. 
The  cloud  and  the  population  are  composed  of  elements 
that  resemble  each  other  in  the  brevity  of  their  exist- 
ence, while  the  general  features  of  the  cloud  and  of  the 
population  are  alike  in  that  they  abide. 

Preliminary  Problem. — The  proportion  of  the 
population  that  dies  at  each  age,  is  well  known,  and  the 
diseases  of  which  they  die  are  also  w^ell  known,  but  the 
statistics  of  hereditary  disease  are  as  yet  for  the  most 
part  contradictory  and  untrustworthy. 

It  is  most  desirable  as  a  preliminary  to  more  minute 
inquiries,  that  the  causes  of  death  of  a  large  number  of 
persons  should  be  traced  during  two  successive  genera- 
tions in  somewhat  the  same  broad  way  that  Stature 
and  several  other  peculiarities  were  traced  in   the  pre- 


166  NATURAL  INHERITANCE.  [chap. 

ceding  chapters.  There  are  a  certain  number  of  recog- 
nized groups  of  disease,  which  we  may  call  A,  B,  C,  &c., 
and  the  proportion  of  persons  who  die  of  these  diseases 
in  each  of  the  two  generations  is  the  same.  The  pre- 
liminary question  to  be  determined  is  whether  and  to 
what  extent  those  who  die  of  A  in  the  second  genera- 
tion, are  more  or  less  often  descended  from  those  who 
died  of  A  in  the  first  generation,  than  would  have  been 
the  case  if  disease  were  neither  hereditarily  transmitted 
nor  clung  to  the  same  families  for  any  other  reason. 
Similarly  as  regards  B,  C,  D,  and  the  rest. 

This  inquiry  would  be  more  difficult  than  those 
hitherto  attempted,  because  longevity  and  fertility  are 
both  affected  by  the  state  of  health,  and  the  circum- 
stances of  home  life  and  occupation  have  a  great  effect 
in  causing  and  in  checking  disease.  Also  because  the 
father  and  mother  are  found  in  some  notable  cases  to 
contribute  disease  in  very  different  degrees  to  their 
male  and  female  descendants. 

I  had  hoped  even  to  the  last  moment,  that  my 
collection  of  Family  Eecords  would  have  contributed 
in  some  small  degree  towards  answering  this  question, 
but  after  many  attempts  I  find  them  too  fragmentary 
for  the  purpose.  It  was  a  necessary  condition  of  success 
to  have  the  completed  life-histories  of  many  Fraternities 
who  were  born  some  seventy  or  more  years  ago,  that 
is,  during  the  earlier  part  of  this  century,  as  well  as 
those  of  their  parents  and  all  their  uncles  and  aunts. 
My  Records  contain  excellent  material  of  a  later  date, 
that  will  be  vahiable  in  future  years  ;   but  they  must 


X.]  DISEASE.  167 

bide  tlieir  time  ;  they  are  insufficient  for  the  period  in 
question.  By  attempting  to  work  with  incompleted  life 
histories  the  risk  of  serious  error  is  incurred. 


Data, — The  Schedule  in  Appendix  G,  which  is  illus- 
trated in  more  detail  by  Tables  A  and  B  that  follow  it, 
shows  the  amount  of  information  that  I  had  hoped  to 
obtain  from  those'  who  were  in  a  -position  to  furnish 
complete  returns.  It  relates  to  the  "Subject"  of  the 
pedigree  and  to  each  of  his  1 4  direct  ancestors,  up  to  the 
great-grandparents  inclusive,  making  in  all  15  persons. 
Also,  to  the  Fraternities  of  which  each  of  these  15  per- 
sons was  a  member.  Eeckoning  the  total  average 
number  of  persons  in  each  fraternity  at  5,  which  is 
under  the  mark  for  my  R.F.F  collection,  questions 
were  thus  asked  concerning  an  average  of  75  different 
persons  in  each  family.  The  total  number  of  the 
Eecords  that  I  am  able  to  use,  is  about  160;  so  the 
aggregate  of  the  returns  of  disease  ought  to  have  been 
about  twelve  thousand,  and  should  have  included  the 
causes  of  death  of  perhaps  6,000  of  them.  As  a  matter  of 
fact,  I  have  only  about  one-third  of  the  latter  number, 

Trustivorthiness  of  R.F.F.  data. — The  first  object  was 
to  ascertain  the  trustworthiness  of  the  medical  informa- 
tion sent  to  me.  There  is  usually  much  disinclination 
among  families  to  allude  to  the  serious  diseases  that 
they  fear  to  inherit,  and  it  was  necessary  to  learn  whether 
this  tendency  towards  suppression  notably  vitiated  the 
returns.     The  test  applied  was  both  simple  and  just. 


168  NATURAL  INHERITANCE.  [chap. 

If  consumption,  cancer,  drink  and  suicide,  appear  among 
tlie  recorded  cases  of  death  less  frequently  than  they  do 
in   ordinary  tables   of  mortality,  then    a   bias   towards 
suppression   could  be  proved  and  measured,  and  would 
have  to  be  reckoned  wnth  ;  otherwise  the  returns  might  be 
accepted  as  being  on  the  whole  honest  and  outspoken. 
T  find  the  latter  to  be  the  case.     Sixteen  per  cent,   of 
the  causes  of  death  (or  1  in  6^)  are  ascribed  to  consump- 
tion,   5    per    cent,    to    cancer,   and    nearly  2  per  cent. 
to  drink  and  to  suicide  respectively.     Insanity  was  not 
specially  asked  about,  as  I   did  not  think  it  wise  to  put 
too  many  disagreeable   questions,  however  it  is   often 
mentioned.     I  dare  say  that  it,  or  at  least  eccentricity, 
is  not   unfrequently  passed  over.     Careful  accuracy  in 
framing  the  replies  appears  to  have  been  the  rule  rather 
than  the  exception.     In  the  preface  to  the  blank  forms 
of  the  Records  of  Family  Faculties  .and  elsewhere,  I  had 
explained  my  objects  so  fully  and  they  were  so  reason- 
able   in    themselves,    that    my    correspondents    have 
evidently  entered  with  interest  into  what  was  asked  for, 
and  shown  themselves  willing  to  trust  me  freely  with 
their  family  histories.     They  seem    generally   to    have 
given  all  that  was  known  to  them,  after  making  much 
search  and  many  inquiries,  and  after  due  references  to 
registers  of  deaths.       The  insufiiciency  of  their  returns 
proceeds  I  feel  sure,  much  less  from  a  desire  to  suppress 
unpleasant  truths  than  from  pure   ignorance,   and  the 
latter  is  in  no  small  part  due  to  the  scientific  ineptitude 
of  the  mass   of  the  members  of  the  medical  profession 
two  and  more  generations   ago,  when  even  the  stetho- 


X.]  DISEASE.  109 

scope  was  unknown.     They  were  then  incompetent  to 
name  diseases  correctly. 

Mixture  of  Inheritances. — The  first  tiling  that  struck 
me  after  methodically  classifying  the  diseases  of  each 
family,  in  the  form  shown  in  the  Schedule,  w^as  their 
great  intermixture.  The  Tables  A  and  B  in  Appendix  Gl- 
are offered  as  ordinary  specimens  of  what  is  everywhere 
to  be  found.  They  are  actual  cases,  except  that  I  have 
given  fancy  names  and  initials,  and  for  further  conceal- 
ment, have  partially  transposed  the  sexes.  Imagine  an 
intermarriage  between  any  two  in  the  lower  division  of 
these  tables,  and  then  consider  the  variety  of  inheritable 
disease  to  wdiicli  their  children  would  be  liable  !  The 
problem  is  rendered  yet  more  complicated  by  the 
metamorphoses  of  disease.  The  disease  A  in  the  parent 
does  not  necessarily  appear,  even  when  inherited,  as  A  in 
the  children.  We  know  very  little  indeed  about  the 
effect  of  a  mixture  of  inheritable  diseases,  how  far  they 
are  mutually  exclusive  and  how  far  they  blend ;  or  how 
far  when  they  blend,  they  change  into  a  third  form. 
Owing  to  the  habit  of  free  inter-marriage  i)o  person  can 
be  exempt  from  the  inheritance  of  a  vast  variety  of 
diseases  or  of  special  tendencies  to  them.  Deaths  by 
mere  old  age  and  the  accompanying  failure  of  vital 
powers  without  any  w^ell  defined  malady,  are  very 
common  in  my  collection,  but  I  do  not  find  as  a  rule, 
that  the  children  of  persons  who  die  of  old  age  have  any 
marked  immunity  from  specific  diseases. 

There  is  a  curious  double  appearance  in  the  Eecords, 


170  NATURAL  INHERITANCE.  [chap. 

tlie  one  of  an  obvions  liereditary  tendency  to  disease 
and  the  other  of  the  reverse.  There  are  far  too  many 
striking  instances  of  coincidence  between  the  diseases  of 
the  parents  and  of  the  children  to  admit  of  reasonable 
doubt  of  their  being  often  inherited.  On  the  other  hand, 
when  I  hide  with  my  hand  the  lower  part  of  a  page  such 
as  those  in  Tables  A  and  B,  and  endeavour  to  make 
a  forecast  of  what  I  shall  find  under  my  hand  after 
studying  the  upper  portion,  I  am  sometimes  greatly  mis- 
taken. Very  unpromising  marriages  have  occasionally 
led  to  good  results,  especially  where  the  parental  disease 
is  one  that  usually  breaks  out  late  in  life,  as  in  the  case 
of  cancer.  The  children  may  then  enjoy  a  fair  length 
of  days  and  die  in  the  end  of  some  other  disease ; 
although  if  that  disease  had  been  staved  off  it  is  quite 
possible  that  the  cancer  would  ultimately  have  appeared. 
I  have  two  remarkable  instances  of  this.  In  one  of 
them,  three  grandparents  out  of  four  died  of  cancer.  In 
each  of  the  fraternities  of  which  the  father  and  mother 
were  members,  one  and  one  person  only,  died  of  it. 
As  to  the  children,  although  four  of  them  have  lived  to 
past  seventy  years,  not  one  has  shown  any  sign  of 
cancer.  The  other  case  differs  in  details,  but  is  equally 
remarkable.  However  diseased  the  parents  may  be,  it 
is  of  course  possible  that  the  children  may  inherit  the 
healthier  constitutions  of  their  remoter  ancestry.  Pro- 
mising looking  marriages  are  occasionally  found  to  lead 
to  a  sickly  progeny,  but  my  materials  are  too  scanty  to 
permit  of  a  thorough  investigation  of  these  cases. 

The    general    conclusion    thus  far   is,   that   owing  to 


X.]  DISEASE.  171 

the  hereditary  tendencies  in  each  person  to  disease 
being  usually  very  various,  it  is  by  no  means  always 
that  useful  forecasts  can  be  made  concerning  the  health 
of  the  future  issue  of  any  couple. 

Consumption. 

General  Remarks. — The  frequency  of  consumption 
in  England  being  so  great  that  one  in  at  least  every  six 
or  seven  persons  dies  of  it,  and  the  fact  that  it  usually 
appears  early  in  life,  and  is  therefore  the  less  likely  to 
be  forestalled  by  any  other  disease,  render  it  an  appro- 
priate subject  for  statistics.  The  fact  that  it  may  be 
acquired,  although  there  has  been  no  decided  hereditary 
tendency  towards  it,  introduces  no  serious  difficulty, 
being  more  or  less  balanced  by  the  opposite  fact  that  it 
may  be  withstood  by  sanitary  precautions  although  a 
strong  tendency  exists.  Neither  does  it  seem  worth 
while  to  be  hypercritical  and  to  dwell  overmuch  on  the 
different  opinions  held  by  experts  as  to  what  constitutes 
consumption.  The  ordinary  symptoms  are  patent 
enough,  and  are  generally  recognized ;  so  we  may  be 
content  at  first  with  lax  definitions.  At  the  same 
time,  no  one  can  be  more  strongly  impressed  than 
myself  with  the  view  that  in  proportion  as  we  desire 
to  improve  our  statistical  work,  so  we  must  be  in- 
creasingly careful  to  divide  our  material  into  truly 
homogeneous  groups,  in  order  that  all  the  cases  con- 
tained in  the  same  group  shall  be  alike  in  every 
important  particular,  difi"ering  only  in  petty  details. 
This  is  far  more  important  than  adding  to  the  number 


172  NATURAL  INHERITANCE.  [chap. 

of  cases.  My  material  admits  of  no  such  delicacy  of 
division  ;  nevertlieless  it  leads  to  some  results  worth 
mentioning. 

In  sorting  my  cases,  I  included  under  the  liead  of 
Consumption  all  tlie  causes  of  death  described  by  one  or 
the  other  following  epithets,  attention  being  also  paid 
to  the  context,  and  to  the  phraseology  used  elsewhere 
by  the  same  writer  : — Consumption  ;  Phthisis  ;  Tuber- 
cular disease  ;  Tuberculosis  ;  Decline  ;  Pulmonary,  or 
lung  disease  ;  Lost  lung ;  Abscess  on  lung ;  Haemorrhage 
of  lungs  (fatal)  ;  Lungs  affected  (here  especially  the 
context  was  considered).  All  of  these  were  reckoned 
as  actual  Consumption. 

In  addition  to  these  there  were  numerous  phrases  of 
doubtful  import  that  excited  more  or  less  reasonable 
suspicion.  It  may  be  that  the  disease  had  not  suffi- 
ciently declared  itself  to  justify  more  definite  language, 
or  else  that  the  phrase  employed  was  a  euphemism  to 
veil  a  harsh  truth.  Paying  still  more  attention  to  the 
context  than  before,  I  classed  these  doubtful  cases 
under  three  heads: — (1)  Highly  suspicious  ;  (2)  Sus23i- 
cious ;  (3)  Somewhat  suspicious.  They  were  so  rated 
that  four  cases  of  the  first  should  be  reckoned  equivalent 
to  three  cases  of  actual  consumption,  four  cases  of  the 
second  to  two  cases,  and  four  of  the  third  to  one  case. 

The  following  is  a  list  of  some  of  the  phrases  so  dealt 
with.  The  occasional  appearance  of  the  same  phrase 
under  different  headings  is  due  to  differences  in  the 
context : — 

1.  Highly  suspicious: — Consumptive  tendency,  Con- 


X.]  DISEASE  173 

sumption  feared,  and  died  of  bad  cliill.  Chest  colds 
with  pleurisy  and  congestion  of  lungs.  Died  of  an 
attack  on  the  chest.  Always  delicate.  Delicate  lungs. 
Haemorrhage  of  lungs.  Loss  of  part  of  lung.  Severe 
pulmonary  attacks  and  chest  affections. 

2.  Suspicious  : — Chest  complaints.  Delicate  chest. 
Colds,  cough  and  bronchitis.  Delicate,  and  died  of 
asthma.     Scrofulous  tendency. 

3.  Somewhat  suspicious  : — Asthma  when  young.  Pul- 
monary congestion.  Not  strong ;  anaemic.  Delicate. 
Colds,  coughs.  Debility  ;  general  weakness.  [The  con- 
text was  especially  considered  in  this  group.] 

Parent  to  Child. — I  have  only  four  cases  in  which  both 
parents  were  consumptive ;  these  will  be  omitted  in  the  fol- 
lowing remarks  ;  but  whether  included  or  not,  the  results 
would  be  unaltered,  for  they  run  parallel  to  the  rest. 

There  are  QQ  marriages  in  which  one  parent  was 
consumptive  ;  they  produced  between  them  413  chil- 
dren, of  whom  70  were  actually  consumptive,  and  others 
who  were  suspiciously  so  in  various  degrees.  When 
reckoned  according  to  the  above  method  of  computation, 
these  amounted  to  37  cases  in  addition,  forming  a  total 
of  107.  In  other  words,  26  per  cent,  of  the  children 
were  consumptive.  Where  neither  parent  was  consump- 
tive, the  proportion  in  a  small  batch  of  well  marked 
cases  that  I  tried,  was  as  high  as  18  or  19  per  cent,  but 
this  is  clearly  too  much,  as  that  of  the  general  population 
is  only  16  per  cent.  Again,  by  taking  each  fraternity 
separately  and  dividing  the  quantity  of  consumption  in 
it  by  the  number  of  its  members,  I  obtained  the  averao;e 


174 


NATURAL  INHERITANCE. 


[chap. 


consumptive  taint  of  each  fraternity.  For  instance,  if 
in  a  fraternity  of  10  members  there  was  one  actually 
consumptive  member  and  four  "somewhat  suspiciously" 
so,  it  would  count  as  a  fraternity  of  ten  members,  of 
whom  two  were  actually  consumptive,  and  the  average 
taint  of  the  fraternity  would  be  reckoned  at  one-fifth 
part  of  the  wdiole  or  as  20  per  cent. 

Treating  each  fraternity  separately  in  this  way,  and 
then  averaging  the  whole  of  them,  the  mean  taint  of 
the  children  of  one  consumptive  parent  was  made  out 
to  be  28  per  cent. 

Distribution  of  Fraternities. — Next  I  arranged  the 
fraternities  in  such  way  as  would  show  whether,  if  we 
reckoned  each  fraternity  as  a  unit,  their  respective 
amounts  of  consumptive  taint  were  distributed  ^'nor- 
mally "  or  not.  The  results  are  contained  ia  line  A  of 
the  following  table  : — 

Percentage  of  Cases  having  various  Percentages  of  Taint. 


Percentages  of  Taint. 

0 

and 

under 

9 

10 

and 

under 

19 

20 

and 

under 

29 

30 

and 

under 

39 

40 

and 

above 

Total. 

A.    66  cases,  one 
parent    con- 
sumptive. 

27 

20 

9 

15 

29 

100 

B.    84  cases,  one 
brother  con- 
sumptive. 

49 

14 

10 

13 

14 

100 

X.]  DISEASE.  175 

They  struck  me  as  so  remarkable,  in  the  way  shortly 
to  be  explained,  that  I  proceeded  to  verify  them  by  as 
different  a  set  of  data  as  my  Records  could  afford.  I 
took  every  fraternity  in  which  at  least  one  member 
was  consumptive,  and  treated  them  in  a  way  that  would 
answer  the  following  question.  "  One  member  of  a 
fraternity,  whose  number  is  unknown,  is  consumptive  ; 
what  is  the  chance  that  a  named  but  otherwise  un- 
known brother  of  that  man  will  be  consumptive  also  ?  " 
The  fraternity  that  was  taken  above  as  an  example, 
would  be  now  reckoned  as  one  of  nine  members,  of 
whom  one  was  actually  consumptive.  There  were  84 
fraternities  available  for  the  present  purpose,  and  the 
results  are  given  in  the  line  B  of  the  table.  The  data 
in  A  and  B  somewhat  overlap,  but  for  the  most  part 
they  differ. 

They  concur  in  telling  the  same  tale,  namely,  that  it 
is  totally  impossible  to  torture  the  figures  so  as  to  make 
them  yield  the  single-humped  "  Curve  of  Frequency  " 
(Fig.  3  p.  38).  They  make  a  distinctly  double-humped 
curve,  whose  outline  is  no  more  like  the  normal  curve 
than  the  back  of  a  Bactrian  camel  is  to  that  of  an 
Arabian  camel.  Consumptive  taints  reckoned  in  this 
way  are  certainly  not  "  normally "  distributed.  They 
depend  mainly  on  one  or  other  of  two  groups  of  causes, 
one  of  which  tends  to  cause  complete  immunity  and 
the  other  to  cause  severe  disease,  and  these  two  groups 
do  not  blend  freely  together.  Consumption  tends  to 
be  transmitted  strongly  or  not  at  all,  and  in  this  respect 
it   resembles  the   baleful   influence    ascribed  to  cousin 


17G  NATURAL  INHERITANCE.  [ciiap. 

marriages,  which  appears  to  be  very  small  when 
statistically  discussed,  but  of  whose  occasional  severity 
most  persons  have  observed   examples. 

I  interpret  these  results  as  showing  that  consumption 
is  largely  acquired,  and  that  the  hereditary  influence  of 
an  acquired  attack  is  small  when  there  is  no  accom- 
panyiag  "malformation."  This  last  phrase  is  intended 
to  cover  not  only  a  narrow  chest  and  the  like,  but  what- 
ever other  abnormal  features  may  supply  the  physical 
basis  upon  which  consumptive  tendencies  depend,  and 
which  I  presume  to  be  as  hereditary  as  any  other 
malformations. 

Severely -tainted  Fraternities. — Pursuing  the  matter 
further,  I  selected  those  fraternities  in  which  consump- 
tion was  especially  frequent,  and  in  which  the  causes  of 
the  deaths  both  of  the  Father  and  of  the  Mother  were 
given.  They  were  14  in  number,  and  contained  be- 
tween them  a  total  of  102  children,  of  whom  rather 
more  than  half  died  before  the  age  of  40.  Though 
records  of  infant  deaths  were  asked  for,  I  doubt  if 
they  have  been  fully  supplied..  As  102  differs  little 
from  100,  the  following  figures  will  serve  as  per- 
centages :  42  died  of  actual  consumption  and  11  others 
of  lung  disease  variously  described.  Only  one  case 
was  described  as  death  from  heart  disease,  but  weakness 
of  the  heart  during  life  was  spoken  of  in  a  few  cases. 
The  remaining  causes  of  death  were  mostly  undescribed, 
and  those  that  were  named  present  no  peculiarity  worth 
notice.     I  then  took  out   the  causes    of  death  of  the 


x.| 


DISEASE. 


177 


Fathers  and  Mothers  and  their  ages  at  death,  and 
severally  classified  them  as  in  the  Table  below.  It 
must  be  understood  that  there  is  nothing  in  the  Table 
to  show  how  the  persons  were  paired.  The  Fathers  are 
treated  as  a  group  by  themselves,  and  the  Mothers  as  a 
separate  group,  also  by  themselves. 


Causes  of  Death  of  the  Parents  of  those  Fraternities  in  which 
Consumption  Greatly  Prevailed. 


Father                            ^S®  ^* 
^^^'^^^'                          death. 

Mother.                  ^^l^^ 
death. 

Order  of 
ages  at  death. 

F.         M. 

Asthma 70 

Bronchitis 89 

Inf.  kidneys  and  bronchitis  .    73 
Abscess  of  liver  through  lung(alive) 

Heart 68 

Heart 74 

Apoplexy 62 

Apoplexy 75 

Apoplexy.    . 78 

Decay 74 

Cancer 52 

Senile  gangrene 76 

(2  bros,  d.  of  cancer). 
Mortification  of  toe     ....    59 
Accident 51 

(3  bros.  and  2  ss.  d.  of  cons.) 

Consumption 40 

Consumption 43 

Consumption 47 

Consumption 55 

Consumption 65 

Consumption 66 

Water  on  chest  ■.    .    .    .60 
Weak  chest ....      (alive) 
(1  br.  and  2  ss.  d.  of  cons. ) 
Haemorrhage  of  lungs    .   44 
Ossification  of  heart   .    .  50 

Nose  bleeding 83 

Cancer 42 

Atrophy 73 

Age 74 

51 
52 
59 
62 
68 
70 
73 
74 
74 
75 
76 
78 
89 

40 
42 
43 
44 
47 
50 
58 
60 
65 
66 
73 
74 
83 

Very  little  account  is  given  of  the  fraternities  to  which  the  fathers  and 
mothers  belong,  and  nothing  of  interest  beyond  what  is  included  in  the  above. 

The  contrast  is  here  most  striking  between  the 
tendencies  of  the  Father  and  Mother  to  transmit  a 
serious  consumptive  taint  to  their  children.  The  cases 
were  selected  without  the  slightest  bias  in  favour  of 
showing  this  result ;  in  fact,  such  is  the  incapacity  to 
see  statistical  facts  clearly  until  they  are  pointed  out, 
that  1  had  no  idea  of  the  extraordinary  tendency  on 


178  NATURAL  INHERITANCE.  [chap. 

tlie  part  of  tlie  mother  to  transmit  consumption,  as 
sliown  in  this  Table,  until  I  had  selected  the  cases  and 
nearly  finished  sorting  them.  Out  of  the  fourteen 
families,  the  mother  was  described  as  actually  dying 
of  consumption  in  six  cases,  of  lung  complaints  in  two 
others,  and  of  having  highly  consumptive  tendencies 
in  another,  making  a  total  of  nine  cases  out  of  the 
fourteen.  On  the  other  hand  the  Fathers  show  hardly 
any  consumptive  taints.  One  was  described  as  of  a 
very  consumptive  fraternity,  though  he  himself  died  of 
an  accident ;  and  another  who  was  still  alive  had  suffered 
from  an  abscess  of  the  liver  that  broke  through  the 
lungs.  Beyond  these  there  is  nothing  to  indicate 
consumption  on  the  Fathers'  side. 

Another  way  of  looking  at  the  matter  is  to  compare 
the  ag^es  at  death  of  the  Mothers  and  of  the  Fathers 
respectively,  as  has  been  done  at  the  side  of  the  Table, 
when  we  see  a  notable  difference  between  them,  the 
Mid-age  of  the  Mothers  being  58,  as  against  73  of 
the  Fathers. 

The  only  other  group  of  diseases  in  my  collection, 
that  affords  a  fair  number  of  instances  in  which  frater- 
nities are  greatly  afiected,  are  those  of  the  Heart. 
The  instances  are  only  nine  in  number,  but  I  give  an 
analysis  of  them,  not  for  any  value  of  their  own,  but 
in  order  to  bring  the  peculiarities  of  the  consumptive 
fraternities  more  strongly  into  relief  by  means  of  com- 
parison. In  one  of  these  there  was  no  actual  death 
from  heart  disease,  though  three  had  weak  hearts  and 
two  others  had  rheumatic  gout  and  fever.     These  nine 


X.] 


DISEASE. 


179 


families  contained  between  them  sixty-nine  children, 
being  at  the  rate  of  7*7  to  a  family.  The  number  of 
deaths  from  heart  disease  was  24 ;  from  ruptured 
blood  vessels,  2  ;  from  consumption  and  lung  disease, 
8  ;  from  dropsy  in  various  forms,  3  ;  from  apoplexy, 
paralysis,    and    epilepsy,    5 ;    from    suicide,    2 ;    from 


Causes  of  Death  of  the  Parents  of  those  Fraternities  in  which 
Heart  Disease  Prevailed. 


Causes  of  death. 

Ages  at  death. 

Order  of 
ages  at  death. 

Father. 

Mother. 

F. 

M. 

Heart 

Apoplexy  and  paralysis    . 

Consumption 

Asthma 

Gout 

Senile  Gangrene     .... 
Tumour  in  liver     .... 

Cancer 

Living 

Unknown    

59,  70 
74,  78 
53 
70 
55 

75 
old. 

61,  63,  74 

62,  70,  72 

si 

77 

85 
2  bros.  and  1  sis. 
d.  of  heart  disease 
and  1  of  paralysis 
cet.  40. 

53 

55 
59 
70 
70 
74 
75 
78 
old. 

61 
62 
63 
70 

72. 
74 
77 
81 
85 

cancer,  1.  There  is  no  obvious  difference  between  the 
diseases  of  their  Fathers  and  Mothers  as  shown  in  the 
Table,  other  than  the  smallness  of  the  number  of  cases 
would  account  for.  Their  mid-ages  at  death  were 
closely  the  same,  70  and  72,  and  the  ages  in  the  two 
groups  run  alike. 

I  must  leave  it  to  medical  men  to  verify  the  amount 
of  truth  that  may  be  contained  in  what  I  have  deduced 
from  these    results    concerning  the  distinctly  superior 

N  2 


180  NATURAL  INHERITANCE.  [chap. 

power  of  the  mother  over  that  of  the  father  to  produce 
a  highly  consumptive  family.  Any  physician  in  large 
practice  among  consumptive  cases  could  test  the  ques- 
tion easily  by  reference  to  his  note-books.  A  "  highly 
consumptive "  fraternity  may  conveniently  be  defined 
as  one  in  which  at  least  half  of  its  members  have 
actually  died  of  consumption,  or  else  are  so  stricken 
that  their  ultimate  deaths  from  that  disease  may  be 
reckoned  upon.  Also  to  avoid  statistical  accidents,  the 
fraternities  selected  for  the  inquiry  should  be  large, 
consisting  say  of  six  children  and  upwards.  Of  course 
the  numerical  proportions  given  by  the  above  14  frater- 
nities are  very  rude  indications  indeed  of  the  results  to 
which  a  thorough  inquiry  might  be  expected  to  lead. 

Accepting  the  general  truth  of  the  observation 
that  consumptive  mothers  produce  highly  consumptive 
families  much  more  commonly  than  consumptive  fathers, 
it  is  easy  to  offer  what  seems  to  be  an  adequate  ex- 
planation. Consumption  is  partly  acquired  by  some 
form  of  contagion  or  infection,  and  is  partly  an  here- 
ditary malformation.  So  far  as  it  is  due  to  the  latter 
in  the  wide  sense  already  given  to  the  word  "  mal- 
formation," it  may  perhaps  be  transmissible  equally  by 
either  parent.  But  so  far  as  it  is  contagious  or 
infectious,  we  must  recollect  that  the  child  is  pecu- 
liarly exposed  during  all  the  time  of  its  existence 
before  birth,  to  contagion  from  its  mother.  Daring 
infancy,  it  lies  perhaps  for  hours  daily  in  its  mother's 
arms,  and  afterwards  lives  much  by  her  side,  closely 
caressed,  and  breathing  the  tainted  air  of  her  sheltered 


X.]  DISEASE.  181 

rooms.  The  ex23lanatioii  of  the  fact  that  we  have 
been  discussing  appears  therefore  to  be  summed  u^  in 
the  single  word — ^Infection. 

Consumptivity .  —  Before    abandoning    the    topic    of 
hereditary   consumption,   it  may  be  well  to  discuss  it 
from    the  same  point    of  view   that    was    taken   when 
discussing    the    artistic    temperament.        Consumption 
being  so  common  in  this  country  that  fully  one  person 
out  of  every  six  or  seven  die  of  it,  and  all  forms  of 
hereditary  disease  being  intermixed  through  marriage, 
it  follows  that  the  whole  population  must  be  n]ore  or 
less  tainted  with  consumption.     That  a  condition  which 
we    may  call    ''  consumptivity,"    for   want  of  a  better 
word,  may  exist  without  showing    any    outward   sign, 
is  proved  by  the  fact  that  as  sanitary  conditions  worsen 
by    ever  so    little,  more  persons    are    affected   by    the 
disease.     It   seems  a  fair  view  to  take,  that  when  the 
amount   of  consumptivity  reaches   a  certain  level,  the 
symptoms    of    consumption    declare    themselves ;    that 
when  it  approaches  but  falls  a  little  short  of  that  level, 
there   are  threatening   symptoms  ;    that  when    it  falls 
far  below  the  level,  there  is  a  fallacious  appearance  of 
perfect  freedom  from  consumptivity.     We  may  reason- 
ably  proceed    on   the    hypothesis    that    consumptivity 
might  somehow  be  measured,  and  that  if  its  measure- 
ment was  made  in  each  of  any  large  group  of  persons, 
the  measures  would  be  distributed  "  normally." 

So  far  we  are  on  fairly  safe    ground,   but  now   un- 
certainties begin  upon   which   my  data  fail    to   throw 


182  NATURAL  INHERITANCE.  [chap. 

sufficient  light.  Longevity,  marriage,  and  fertility 
must  all  be  affected  by  the  amount  of  consumptivity, 
whereas  in  the  case  of  the  faculties  hitherto  discussed 
they  are  not  affected  to  any  sensible  extent.  It  how- 
ever happens  that  these  influences  tend  to  neutralize 
one  another.  It  is  true  that  consumptive  persons  die 
early,  and  many  of  them  before  a  marriageable  age. 
On  the  other  hand,  they  certainly  marry  earlier  as  a 
rule  than  others,  one  cause  of  which  lies  in  their 
frequent  great  attractiveness ;  and  again,  when  they 
marry,  they  produce  children  more  quickly  than  others. 
Consequently  those  who  die  even  long  before  middle 
age,  often  contrive  to  leave  large  families.  The  greater 
rapidity  with  which  the  generations  follow  each  other, 
is  also  a  consideration  of  some  importance.  There 
is  therefore  a  fair  doubt  whether  a  group  of  young 
persons  destined  to  die  of  consumption,  contribute 
considerably  less  to  the  future  population  than  an 
equally  large  group  who  are  destined  to  die  of  other 
diseases,  I  will  at  all  events  assume  that  consumptivity 
does  not  affect  the  numbers  of  the  adult  children, 
simply  as  a  working  hypothesis,  and  will  afterwards 
compare  its  results  with  observed  facts. 

I  should  add  that  the  question  whether  the  sexes 
transmit  consumption  equally,  lies  outside  the  present 
w^ork,  at  least  for  practical  purposes ;  for  whether  they 
transmit  it  equally  or  not  would  not  affect  the  results 
materially.  Our  list  of  data  is  therefore  limited  to 
these: — that  16  per  cent,  of  the  population  die  of 
consumption,    that    consumptivity   is   normally    distri- 


X.]  DISEASE.  183 

buted,  and  that  tlie  law  of  hereditary  regression  from 
a  deviation  of  three  units  on  the  part  of  either 
parent  to  an  average  of  one  unit  in  the  child,  may 
be  supposed  to  apply  here,  just  as  it  did  to  Stature 
and  to  the  other  subjects  of  the  preceding  chapters. 

Let  the  scale  by  which  consumptivity  is  measured  be 
such  that  the  Q  of  the  general  population  =  1.  Let 
its  IVI  =  N,  when  measured  on  the  same  scale  ;  the 
value  of  N  is  and  will  remain  unknown.  Let  N  +  C 
be  the  number  of  units  of  consumptivity  that  just 
amount  to  actual  consumption.  Our  data  tell  us  that 
16  per  cent,  of  the  population  have  an  amount  of  con- 
sumptivity that  exceeds  N  +  C.  On  referring  to 
Table  8,  w^e  find  the  value  of  C  that  corresponds  to  the 
Grade  of  (100°— 16°),  or  of  84°,  to  be  1-47.  There- 
fore whenever  the  consumptivity  of  a  person  exceeds 
N  +   1*47,  he  has  actual  consumption. 

Adding  together  the  tabular  values  in  Table  8  at  all 
the  odd  grades  above  84°,  we  shall  find  their  average 
value  to  be  2*23.  We  may  therefore  assume  (see  p.  160) 
that  a  group  of  persons  each  of  whom  has  a  consumpt- 
ivity of  N  +  2*23  will  approximately  represent  all  the 
grades  above  84°.  The  Co-Fraternity  descended .  from 
such  a  group  will  have  an  IVI  whose  value  according 
to  the  law  of  Eegression  ought  to  be  [N  -f-  ^  (2*23)] 
or  [N  +  0-74  units.] 

Those  members  of  the  Co-Fraternity  are  consumptive 
whose  consumptivity  exceeds  N  -j-  1*47  ;  these  are  the 
same  as  those  whose  deviation  from  [N-l-0'74]  which 
is  the    IVI    of  the    Co-Fraternity,  exceeds  -h  073   unit. 


184  NATURAL  INHERITANCE.  [cHAr. 

Let  tlie  Q  of  the  Co-Fraternity  be  called  n.  The  Grade 
at  which  this  amount  of  deviation  occurs  should  be 
found  in  Table  8  opposite  to  the  value  of  073  divided 
by  n. 

Next  as  regards  the  value  to  be  assigned  to  n,  we 
may  be  assured  that  the  Q  of  a  Co-Fraternity  cannot 
exceed  that  of  the  general  population.  Therefore  n 
cannot  exceed  1.  In  the  case  of  Stature  the  relation 
between  the  Q  of  the  Co-Fraternity  and  that  of  the 
Population  was  found  to  be  as  1 5  to  1 7.  If  the  same 
proportion  held  good  here,  its  value  would  be  0"9. 
This  is  I  think  too  high  an  estimate  for  the  following 
reasons.  The  variability  of  the  Co-Fraternity  depends 
on  two  groups  of  causes.  First,  on  fraternal  variability  ; 
which  itself  is  due  in  part  to  mixed  ancestry,  and  in 
part  to  variety  of  nurture  in  the  same  Fraternity,  both 
before  as  well  as  after  birth.  Secondly,  it  depends  upon 
the  variety  of  ancestry  and  nurture  in  different  Frater- 
nities. As  to  the  first  of  the  two  groups  of  causes, 
they  seem  to  affect  consumptive  fraternities  in  the  same 
way  as  others,  but  not  so  with  respect  to  the  second 
group.  The  household  arrangements  of  vigorous,  of 
moderately  vigorous,  and  of  invalided  parents  are 
not  alike.  I  have  already  spoken  of  infection.  There 
is  also  a  tradition  in  families  that  are  not  vio^orous,  of 
the  necessity  of  avoiding  risks  and  of  never  entering 
professions  that  involve  physical  hardship.  There  is 
no  such  tradition  in  families  who  are  vigorous.  Thus 
there  must  be  much  greater  variability  in  the  environ- 
ments of  a  group  of  persons  taken  from  the  population 


X.]  DISEASE.  185 

at  large,  than  there  is  in  a  group  of  consumptive 
families.  It  would  be  quite  fair  to  estimate  the  value 
of  n  at  least  as  low  as  0'8. 

We  have  thus  three  values  of  n  to  try;  viz.  1,  0*9, 
and  0*8,  of  which  the  first  is  scarcely  possible  and  the 
last  is  much  the  more  suitable  of  the  other  two.  The 
corresponding  values  of  0'73  divided  by  7i,  are  +  0.73, 
+  O'Sl,  and  +  0'91.  Eeferring  to  Table  8  we  find  the 
Grades  corresponding  to  those  deviations  to  be  69,  71, 
and  73.  We  should  therefore  expect  69,  71,  or  73 
per  cent,  of  the  Co-Fraternit}^  to  be  non-consumptive, 
according  to  the  value  of  n  we  please  to  adopt,  and 
the  complement  to  those  percentages,  viz.  31,  29,  or  27, 
to  be  consumptive.  Observation  (p.  173),  gave  the  value 
of  26  by  one  method  of  calculation,  and  of  28  by 
another. 

Too  much  stress  must  not  be  laid  on  this  coincidence, 
because  many  important  points  had  to  be  slurred  over, 
as  already  explained.  Still,  the  prima  facie  result  is 
successful,  and  enables  us  to  say  that  so  far  as  this 
evidence  goes,  the  statistical  method  we  have  employed 
in  treating  consumptivity  seems  correct,  and  that  the 
law  of  heredity  found  to  govern  all  the  difierent  faculties 
as  yet  examined,  appears  to  govern  that  of  consump- 
tivity also,  although  the  constants  of  the  formula  difi'er 
slightly. 

Data  for  Hereditary  Diseases. — The  knowledge  of 
the  officers  of  Insurance  Companies  as  to  the  average 
value  of  unsound  lives  is  by  the  confession  of  many  of 


186  NATURAL  INHERITANCE.  [chap.  x. 

them  far  from  being  as  exact  as  is  desirable.  [See,  for 
example,  tlie  discussion  on  a  memoir  by  G.  Humphreys, 
Actuary  to  the  Eagle  Insurance  Company,  read  before 
the  Institute  of  Actuaries. — Insur.  Mag.  xviii.  p.  178.] 

Considering  the  enormous  money  value  concerned,  it 
would  seem  well  worth  the  while  of  the  higher  class 
of  those  offices  to  combine  in  order  to  obtain  a  collec- 
tion of  completed  cases  for  at  least  two  generations,  or 
better  still,  for  three  ;  such  as  those  in  Examples  A  and 
B,  Appendix  G,  but  much  fuller  in  detail.  Being  com- 
pleted and  anonymous,  there  could  be  little  objection 
on  the  score  of  invaded  privacy.  They  would  have  no 
perceptible  effect  on  the  future  insurances  of  descend- 
ants of  the  families,  even  if  these  were  identified,  and 
they  would  lay  the  basis  of  a  very  much  better 
knowledge  of  hereditary  disease  than  we  now  possess, 
serving  as  a  step  for  fresh  departures.  A  main  point 
is  that  the  cases  should  not  be  picked  and  chosen  to 
support  any  theor}",  but  taken  as  they  come  to  hand. 
There  must  be  a  vast  amount  of  good  material  in 
existence  at  the  command  of  the  medical  officers  of 
Insurance  Companies.  If  it  were  combined  and  made 
freely  accessible,  it  would  give  material  for  many 
years'  work  to  competent  statisticians,  and  would  be 
certain,  judging  from  all  experience  of  a  like  kind, 
to  lead  to  unexpected  results. 


CHAPTER   XL 


LATENT    ELEMENTS. 


Latent   Elements    not    very   numerous. — Pure    Breed. — Simplification  of 

Hereditary  Inquiry. 

Latent  Elements  not  very  numerous. — It  is  not 
possible  tliat  more  than  one  half  of  the  varieties 
and  number  of  each  of  the  parental  elements,  latent 
or  personal,  can  on  the  average  subsist  in  the  off- 
spring. For  if  every  variety  contributed  its  repre- 
sentative, each  child  would  on  the  average  contain 
actually  or  potentially  twice  the  variety  and  twice  the 
number  of  the  elements  (whatever  they  may  be)  that 
were  possessed  at  the  same  stage  of  its  life  by  either 
of  its  parents,  four  times  that  of  any  one  of  its 
grandparents,  1024  times  as  many  as  any  one  of 
its  ancestors  in  the  10th  degree,  and  so  on,  which  is 
absurd.  Therefore  as  regards  any  variety  of  the  entire 
inheritance,  whether  it  be  dormant  or  personal,  the 
chance  of  its  drojDping  out  must  on  the  whole  be  equal 
to  that  of  its  being  retained,  and  only  one  half  of  the 
varieties  can  on  the  average  be  passed  on  by  inherit- 


188  NATURAL  INHERITANCE.  [chap. 

ance.  Now  we  have  seen  that  the  personal  heritage 
from  either  Parent  is  one  quarter,  therefore  as  the  total 
heritage  is  one  half,  it  follows  that  the  Latent  Elements 
must  follow  the  same  law  of  inheritance  as  the  Personal 
ones.  In  other  words,  either  Parent  must  contribute 
on  the  average  only  one  quarter  of  the  Latent 
Elements,  the  remainder  of  them  dropping  out  and 
their  breed  becoming  absolutely  extinguished. 

There  seems  to  be  much  confusion  in  current  ideas 
about  the  extent  to  which  ancestral  qualities  are 
transmitted,  supposing  that  what  occurs  occasionally 
must  occur  invariably.  If  a  maternal  grandparent  be 
found  to  contribute  some  particular  quality  in  one 
case,  and  a  paternal  grandparent  in  another,  it  seems 
to  be  argued  that  both  contribute  elements  in  every 
case.  This  is  not  a  fair  inference,  as  will  be  seen  by 
the  following  illustration.  A  pack  of  playing  cards 
consists,  as  we  know,  of  13  cards  of  each  sort — hearts, 
diamonds,  spades,  and  clubs.  Let  these  be  shuffled 
together  and  a  batch  of  13  cards  dealt  out  from  them, 
forming  the  deal,  No.  1.  There  is  not  a  single  card 
in  the  entire  pack  that  may  not  appear  in  these  13, 
but  assuredly  they  do  not  all  appear.  Again,  let  the 
13  cards  derived  from  the  above  pack,  which  we  will 
suppose  to  have  green  backs,  be  shuffled  with  another 
13  similarly  obtained  from  a  pack  with  blue  backs, 
and  that  a  deal.  No.  2,  of  13  cards  be  made  from  the 
combined  batches.  The  result  will  be  of  the  same  kind 
as  before.  Any  card  of  either  of  the  two  original 
packs  may  be  found  in  the  deal,  No.  2,  but  certainly 


XL]  LATENT  ELEMENTS.  189 

not  all  of  tliem.  So  I  conceive  it  to  be  with  hereditary 
transmission.  No  given  pair  can  possibly  transmit  the 
whole  of  their  ancestral  qualities ;  on  the  other  hand, 
there  is  probably  no  description  of  ancestor  whose 
qualities  have  not  been  in  some  cases  transmitted  to 
a  descendant. 

The  fact  that  certain  ancestral  forms  persist  in  breaking 
out,  such  as  the  zebra-looking  stripes  on  the  donkey, 
is  no  argument  against  this  view.  The  reversion  may 
fairly  be  ascribed  to  precisely  the  same  cause  that  makes 
it  almost  impossible  to  wholly  destroy  the  breed  of 
certain  weeds  in  a  garden,  inasmuch  as  they  are  prolific 
and  very  hardy,  and  wage  successful  battle  with  their 
vegetable  competitors  whenever  they  are  not  heavily 
outmatched  in  numbers. 

If  the  Personal  and  Latent  Elements  are  transmitted 
on  the  average  in  equal  numbers,  it  is  difficult  to 
suppose  that  there  can  be  much  difference  in  their 
variety. 

Pure  Breed. — In  a  perfectly  pure  breed,  maintained 
during  an  indefinitely  long  period  by  careful  selection, 
the  tendency  to  regress  towards  the  M  of  the  general 
population,  would  disappear,  so  far  as  that  tendency 
may  be  due  to  the  inheritance  of  mediocre  ancestral 
qualities,  and  not  to  causes  connected  with  the  relative 
stability  of  different  types.  The  Q  of  Fraternal  Devia- 
tions from  their  respective  true  Mid-Fraternities  which 
we  called  6,  would  also  diminish,  because  it  is  partly 
dependent  on  the  children  in  the  same  family  taking 


190  NATURAL  INHERITANCE.  [chap 

variously  after  different  and  unlike  progenitors.  But 
tlie  difference  between  5  in  a  mixed  breed  such  as  we 
have  been  considering,  and  the  value  whicli  we  may 
call  /3,  wliich  it  would  have  in  a  pure  breed,  would  be 
very  small.  Suppose  the  Prob:  Error  of  the  implied 
Stature  of  each  separate  Grand-Parent  to  be  even  as 
great  as  the  Q  of  the  general  Population,  which  is  17 
inch  (it  would  be  less,  but  we  need  not  stop  to  discuss 
its  precise  value),  then  the  Prob  :  Error  of  the  implied 
Mid-Grand-Parental  stature  would  be  \/ J  x  1'7  inch,  or 
say  0*8  inch.  The  share  of  this,  which  would  on  the 
average  be  transmitted  to  the  child,  would  be  only  ^  as 
much,  or  0'2.  From  all  the  higher  Ancestry,  put 
together,  the  contribution  would  be  much  less  even  than 
this  small  value,  and  we  may  disregard  it.  It  results 
that  ¥  is  a  trifle  greater  than  ^8^  4-0*04.  But  6  =  1'0; 
therefore  13  is  only  a  trifle  less  than  0*98. 

Simplification  of  Hereditary  Inquiry.  —  These 
considerations  make  it  probable  that  inquiries  into 
human  heredity  may  be  much  simplified.  They  assure 
us  that  the  possibilities  of  inheritance  are  not  likely  to 
differ  much  more  than  the  varieties  actually  observed 
among  the  members  of  a  large  Fraternity.  If  then  we 
have  full  life-histories  of  the  Parents  and  of  numerous 
Uncles  and  Aunts  on  both  sides,  we  ought  to  have  a 
very  fair  basis  for  hereditary  inquiry.  Information  of 
this  limited  kind  is  incomparably  more  easy  to  obtain 
than  that  which  I  have  hitherto  striven  for,  namely, 
family   histories     during   four    successive    generations. 


XI.]  LATENT  ELEMENTS.  191 

When  tlie  "  cliildren  "  in  the  pedigree  are  from  40  to 
55  years  of  age,  their  own  life-histories  are  sufficiently 
advanced  to  be  useful,  though  they  are  incomplete, 
and  it  is  still  easy  for  them  to  compile  good  histories 
of  their  Parents,  Uncles,  and  Aunts.  Friends  who 
knew  them  all  would  still  be  aliYC,  and  numerous 
documents  such  as  near  relations  or  personal  friends 
preserve,  but  which  are  mostly  destroyed  at  their 
decease,  would  still  exist.  If  I  were  undertaking 
a  fresh  inquiry  in  order  to  verify  and  to  extend  my 
previous  work,  it  would  be  on  this  basis.  I  should  not 
care  to  deal  with  any  family  that  did  not  number  at 
least  six  adult  children,  and  the  same  number  of  uncles 
and  aunts  on  both  the  paternal  and  maternal  sides. 
Whatever  could  be  learnt  about  the  grandparents 
and  their  brothers  and  sisters,  would  of  course  be 
acceptable,  as  throwing  further  light.  I  should  how- 
ever expect  that  the  peculiarities  distributed  among 
any  large  Fraternity  of  Uncles  and  Aunts  would  fairly 
indicate  the  variety  of  the  Latent  Elements  in  the 
Parent.  The  complete  heritage  of  the  child,  on  the 
average  of  many  cases,  might  then  be  assigned  as 
follows  :  One  quarter  to  the  personal  characteristics  of 
the  Father ;  one  quarter  to  the  average  of  the  personal 
characteristics  of  the  Fraternity  taken  as  a  whole,  of 
whom  the  Father  was  one  of  the  members;  and  similarly 
as  regards  the  Mother's  side. 


CHAPTEE  XIL 

SUMMARY 

The  investigation  now  concluded  is  based  on  tlie  fact 
tliat  the  characteristics  of  any  population  that  is  in 
harmony  with  its  environment,  may  remain  statistically 
identical  durino;  successive  orenerations.  This  is  true 
for  every  characteristic  whether  it  be  affected  to  a  great 
degree  by  a  natural  selection,  or  only  so  slightly  as  to 
be  practically  independent  of  it.  It  was  easy  to  see 
in  a  vague  way,  that  an  equation  admits  of  being  based 
on  this  fact  ;  that  the  equation  might  serve  to  suggest 
a  theory  of  descent,  and  that  no  theory  of  descent  that 
failed  to  satisfy  it  could  possibly  be  true. 

A  large  part  of  the  book  is  occupied  with  preparations 
for  putting  this  equation  into  a  working  form.  Obstacles 
in  the  way  of  doing  so,  which  I  need  not  recapitulate, 
appeared  on  every  side  ;  they  had  to  be  confronted  in 
turns,  and  then  to  be  either  evaded  or  overcome.  The 
final  result  was  that  the  higher  methods  of  statistics, 
which  consist  in  applications  of  the  law  of  Frequency 
of  Error,  were  found  eminently  suitable  for  expressing 


CHAP.  XII.]  SUMMARY.  193 

the  processes  of  heredity.  By  their  aid,  the  desired 
equation  was  thrown  into  an  exceedingly  simple  form 
of  approximative  accuracy,  and  it  became  easy  to 
compare  both  it  and  its  consequences  with  the  varied 
results  of  observation,  and  thence  to  deduce  numerical 
results. 

A   brief  account   of  the    chief   hereditary   processes 
occupies  the  first  part  of  the  book.     It  was   inserted 
principally  in  order  to  show  that  a  reasonable  a  priori 
probability  existed,  of  the  law  of  Frequency  of  Error 
being  found  to  apply  to  them.     It  was  not  necessary  for 
that  purpose  to   embarrass  ourselves  with   any  details 
of  theories  of  heredity  beyond   the  fact,   that  descent 
either  was  particulate  or  acted  as  if  it  were  so.     I  need 
hardly  say  that   the   idea,   though    not  the   phrase   of 
particulate  inheritance,  is  borrowed  from  Darwin's  pro- 
visional theory  of  Pangenesis,  but  there  is  no  need  in 
the  present  inquiry  to  borrow  more  from   it.     Neither 
is  it  requisite  to  take  Weissmann's  views  into  account, 
unless  I  am  mistaken  as  to  their  scope.     It  is  freely 
conceded  that  particulate  inheritance  is  not   the  only 
factor   to   be   reckoned   with  in  a  complete  theory  of 
heredity,  but  that  the  stability  of  the  organism  has  also 
to  be  regarded.     This  may  perhaps  become   a  factor  of 
great  importance  in  forecasting  the  issue  of  highly  bred 
animals,  but  it  was  not  found  to  exercise  any  sensible 
influence  on  those  calculations  with  which  this  book  is 
chiefly  concerned.    Its  existence  has  therefore  been  only 
noted,  and  not  otherwise  taken  into  account. 

The  data  on  which  the  results  mainly  depend  had  to  be 

0 


194  NATURAL  INHERITANCE.  [chap. 

collected  specially,  as  no  suitable  material  for  the  purpose 
was,  so  far  as  I  know,  in  existence.  This  was  done  by 
means  of  an  offer  of  prizes  some  years  since,  that  placed 
in  my  hands  a  collection  of  about  160  useful  Family 
Records.  These  furnished  an  adequate  though  only 
just  an  adequate  supply  of  the  required  data.  In  order 
to  show  the  degree  of  dependence  that  might  be  placed 
on  them  they  were  subjected  to  various  analyses,  and 
the  result  proved  to  be  even  more  satisfactory  than 
might  have  been  fairly  hoped  for.  Moreover  the  errors 
in  the  Records  probably  affect  different  generations  in 
the  same  way,  and  would  thus  be  eliminated  from  the 
comparative  results. 

As  soon  as  the  character  of  the  problem  of  Filial  descent 
had  become  well  understood,  it  was  seen  that  a  general 
equation  of  the  same  form  as  that  by  which  it  was 
expressed,  also  expressed  the  connection  between  Kins- 
men in  every  degree.  The  unexpected  law  of  universal 
Regression  became  a  theoretical  necessity,  and  on 
appealing  to  fact  its  existence  was  found  to  be  con- 
spicuous. If  the  word  "peculiarity"  be  used  to  signify 
the  difference  between  the  amount  of  any  faculty  pos- 
sessed by  a  man,  and  the  average  of  that  possessed 
by  the  population  at  large,  then  the  law  of  Regression 
may  be  described  as  follows.  Each  peculiarity  in  a  man 
is  shared  by  his  kinsmen,  but  on  the  average  in  a  less 
deg:ree.  It  is  reduced  to  a  definite  fraction  of  its 
amount,  quite  independently  of  what  its  amount  might 
be.  The  fraction  differs  in  different  orders  of  kinship, 
becoming  smaller  as  they  are  more  remote.     When  the 


XII.]  SUMMARY.  195 

kinsliip  is  so  distant  that  its  effects  are  not  worth,  taking 
into  account,  the  peculiarity  of  the  man,  however  re- 
markable it  may  have  been,  is  reduced  to  zero  in  his 
kinsmen.  This  apparent  paradox  is  fundamentally  due 
to  the  greater  frequency  of  mediocre  deviations  than  of 
extreme  ones,  occurring  between  limits  separated  by 
equal  widths. 

Two  causes  affect  family  resemblance ;  the  one  is 
Heredity,  the  other  is  Circumstance.  That  which  is 
transmitted  is  only  a  sample  taken  partly  through  the 
operation  of  "accidents,"  out  of  a  store  of  otherwise  un- 
used material,  and  circumstance  must  always  play  a 
large  part  in  the  selection  of  the  sample.  Circumstance 
comprises  all  the  additional  accidents,  and  all  the  pecu- 
liarities of  nurture  both  before  and  after  birth,  and  every 
influence  that  may  conduce  to  make  the  characteristics 
of  one  brother  differ  from  those  of  another.  The 
circumstances  of  nurture  are  more  varied  in  Co -Fra- 
ternities than  in  Fraternities,  and  the  Grandparents 
and  previous  ancestry  of  members  of  Co-Fraternities 
differ;  consequently  Co-Fraternals  differ  among  them- 
selves more  widely  than  Fraternals. 

The  average  contributions  of  each  separate  ancestor 
to  the  heritage  of  the  child  were  determined  apparently 
within  narrow  limits,  for  a  couple  of  generations  at 
least.  The  results  proved  to  be  very  simple;  they 
assign  an  average  of  one  quarter  from  each  parent, 
and  one  sixteenth  from  each  grandparent.  According 
to  this  geometrical  scale  continued  indefinitely  back- 
wards,   the    total    heritage    of    the    child    would    be 

o  2 


196  NATURAL  INHERITANCE.  [chap 

accounted  for,  but  the  factor  of  stability  of  type  has 
to  be  reckoned  witli,  and  this  has  not  yet  been 
adequately  discussed. 

The  ratio  of  filial  Eegression  is  found  to  be  so  bound 
up  with  co-fraternal  variability,  that  when  either  is 
given  the  other  can  be  calculated.  There  are  no 
means  of  deducing  the  measure  of  fraternal  variability 
solely  from  that  of  co-fraternal.  They  differ  by  an  element 
of  which  the  value  is  thus  far  unknown.  Consequently 
the  measure  of  fraternal  variability  has  to  be  calculated 
separately,  and  this  cannot  be  done  directly,  owing  to 
the  small  size  of  human  families.  Four  different  and 
indirect  methods  of  attacking  the  problem  suggested 
themselves,  but  the  calculations  were  of  too  delicate  a 
kind  to  justify  reliance  on  the  E.F.F.  data.  Separate 
and  more  accurate  measures,  suitable  for  the  purpose, 
had  therefore  to  be  collected.  The  four  problems  were 
then  solved  by  their  means,  and  although  different 
groups  of  these  measures  had  to  be  used  with  the 
different  problems,  the  results  were  found  to  agree 
together. 

The  problem  of  expressing  the  relative  nearness  of 
different  degrees  of  kinship,  down  to  the  point  where 
kinship  is  so  distant  as  not  to  be  worth  taking  into 
account,  was  easily  solved.  It  is  merely  a  question  of 
the  amount  of  the  Eegression  that  is  appropriate  to  the 
different  degrees  of  kinship.  This  admits  of  being 
directly  observed  when  a  sufficiency  of  data  are  acces- 
sible, or  else"  of  being  calculated  from  the  values  found 
in  this  inquiry.     A  table  of  these  Eegressions  was  given. 


XII.]  SUMMARY.  197 

Finally,  considerations  were  oflfered  to  show  that 
latent  elements  probably  follow  the  same  law  as  personal 
ones,  and  that  though  a  child  may  inherit  qualities  from 
any  one  of  his  ancestors  (in  one  case  from  this  one,  and 
in  another  case  from  another),  it  does  not  follow  that  the 
store  of  hidden  property  so  to  speak,  that  exists  in  any 
parent,  is  made  up  of  contributions  from  all  or  even 
very  many  of  his  ancestry. 

Two  other  topics  may  be  mentioned.  Eeason 
was  given  in  p.  16  why  experimenters  upon  the 
transmission  of  Acquired  Faculty  should  not  be  dis- 
couraged on  meeting  with  no  affirmative  evidence 
of  its  existence  in  the  first  generation,  because  it 
is  among  the  grandchildren  rather  than  among  the 
children  that  it  should  be  looked  for.  Again,  it  is 
hardly  to  be  expected  that  an  acquired  faculty,  if 
transmissible  at  all,  would  be  transmitted  without  dilu- 
tion. It  could  at  the  best  be  no  more  than  a  variation 
liable  to  Eegression,  which  would  probably  so  much 
diminish  its  original  amount  on  passing  to  the  grand- 
children as  to  render  it  barely  recognizable.  The 
difficulty  of  devising  experiments  on  the  transmission 
of  acquired  faculties  is  much  increased  by  these 
considerations. 

The  other  subject  to  be  alluded  to  is  the  funda- 
mental distinction  that  may  exist  between  two 
couples  whose  personal  faculties  are  naturally  alike. 
If  one  of  the  couples  consist  of  two  gifted  mem- 
bers of  a  poor  stock,  and  the  other  of  two  ordinary 
members    of  a   gifted    stock,     the   difference   between 


198  NATURAL  INHERITANCE.  [chap.  xii. 

them  will  betray  itself  in  their  offspring.  The  children 
of  the  former  will  tend  to  regress ;  those  of  the  latter 
will  not.  The  value  of  a  good  stock  to  the  well- 
being  of  future  generations  is  therefore  obvious,  and 
it  is  well  to  recall  attention  to  an  early  sign  by 
which  we  may  be  assured  that  a  new  and  gifted 
variety  possesses  the  necessary  stability  to  easily 
originate  a  new  stock.  It  is  its  refusal  to  blend 
freely  with  other  forms.  Some  among  the  members 
of  the  same  fraternity  might  possess  the  character- 
istics in  question  with  much  completeness,  and  the 
remainder  hardly  or  not  at  all.  If  this  alternative 
tendency  was  also  witnessed  among  cousins,  there 
could  be  little  doubt  that  the  new  variety  was  of  a 
stable  character,  and  therefore  capable  of  being  easily 
developed  by  interbreeding  into  a  pure  and  durable 
race. 


TABLES. 


Table  1. 


Strength  of  Pull. 

519  Males  aged  23-26. 

From  mea sures  made  at  the  International  Health  Exhibition  in  1884. 

Strength  of  Pull. 

No.  of  cases 
observed. 

Percentages. 

No.  of  cases 
observed. 

Sums  from 
beginning. 

Under  50  lbs. 

10 

2 

2 

„       60    ,, 

42 

8 

10 

„      70    „ 

140 

27 

37 

,,       80    „ 

168 

33 

70 

„       90    „ 

113 

21 

91 

„     100    „ 

22 

4 

95 

Above  100    ,, 

24 

5 

100 

Total 

519 

100 

200 


NATURAL  INHERITANCE. 


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202 


NATURAL  mHERITANCE. 


Tables  4  to  8  inclusive  give  data  for  drawing  Normal  Curves 
of  Frequency  and  Distribution.  They  also  show  the  way  in 
which  the  latter  is  derived  from  the  values  of  the  Probability 
Integral. 

The  equation  for  the  Probablity  Curve^  is  y  =  k  e  in  which 

A  is  "th-e   Measure  of  Precision."      By  taking  ^  and  h  each   as 
unity,  the  values  in  Table  4  are  computed. 


Table  4. 

Data  for  a  Normal  Curve  of  Frequency. 


y 

=  e 

X 

y 

X 

y 

X 

y 

X 

y 

0 

1-00 

± 

10 

0-37 

±  2-0 

0-0183 

±   3-0 

0-0001 

± 

0-2 

0-96 

± 

1-2 

0 

23 

±  2-2 

0-0079 

± 

0-4 

0-85 

± 

1-4 

0 

14 

±  2-4 

0-0032 

±   infi- 

0-0000 

± 

0-6 

0-70 

± 

1-6 

0 

78 

±2-6 

0-0012 

nity 

± 

0-8 

0-53 

± 

1-8 

0-40 

±  2-8 

0-0004 

Table  5. 

2  r*  -f2 

Values  of  the  Probability  Integral, — =  I    e 


cU,  for  Argument  t. 


t{=hx) 

•0 

•1 

•2 

-3 

•4 

•5 

-6 

•7 

•8 

-9 

.1 

2-0 
infinite 

0-00 

0-843 

-9953 

1-0000 

0-11 

0-880 
•9970 

0-22 
0  910 
-9981 

0-33 

0-934 

■9989 

0-43 

0-952 

•9993 

0-52 

0-966 

-9996 

0-60 

0-976 

•9998 

0-68 
0-984 
9999 

0-74 

0-989 

•9999 

0-80 

0-923 

•9999 

When  t  =  '4769  the   corresponding  tabular   entry  would  be  '50; 
therefore,  '4769  is  the  value  of  the  "  Probable  Error." 

1  See  Merriman  O71  the  Method  of  Least  Squares  (Macmillan,  1885),  pp.  26,  186, 
where  fuller  Tables  than  4,  5,  and  6  \Aill  be  found 


TABLES. 


20: 


Table  6. 

Yalues  of  the  Probability  Integral  for  Argument  q^^j^',  that  is,  when  the  unit 
of  measurement  =  the  Probable  error. 


Multiples 

of  the 

•0 

•1 

•2 

•3 

•4 

•5 

•6 

•7 

•8 

•9 

Probable 

Error. 

0 

0-00 

0-65 

0-11 

0-16 

0-21 

0-26 

0-31 

0-36 

0-41 

0-46 

1-0 

•50 

•54 

'58 

•62 

•66 

•69 

••72 

•75 

•78 

•80 

2-0 

•82 

•84 

•86 

.88 

•89 

•91 

•92 

•93 

•94 

•95 

3-0 

•957 

.964 

•969 

•974 

•978 

•982 

•985 

•987 

•990 

•992 

4-0 

•9930 

.9943 

•9954 

•9963 

•9970 

•9976 

•9981 

•9985 

•9988 

•9990 

5-0 
infinite 

•9993 
1^000 

•9994 

•9996 

•9997 

•9997 

•9998 

•9998 

•9999 

•9999 

•9999 

Tables  5  and  6  show  the  proportion  of  cases  in  any  Normal 
system,  in  which  the  amount  of  Error  lies  within  various  extreme 
values,  the  total  number  of  cases  being  reckoned  as  1  'O.  Here  no  re- 
gard is  paid  to  the  sign  of  the  Error,  whether  it  be  plus  or  minus,  but 
its  amount  is  alone  considered.  The  unit  of  the  scale  by  which  the 
Errors  are  measured,  differs  in  the  two  Tables.  In  Table  5  it  is 
the  "  Modulus,"  and  the  result  is  that  the  Errors  in  one  half  of  the 
cases,  that  is  in  0  50  of  them  lie  within  the  extreme  value  (found  by 
interpolation)  of  0*4769,  while  the  other  half  exceed  that  value. 
In  Table  6  the  unit  of  the  scale  is  0'4769.  It  is  derived  from  Table 
5  by  dividing  all  the  tabular  entries  by  that  amount.  Consequently 
one  half  of  the  cases  have  Errors  that  do  not  exceed  1*0  in  terms  of 
the  new  unit,  and  that  unit  is  the  Probable  Error  of  the  System. 
It  will  be  seen  in  Table  6  that  the  entry  of  "50  stands  opposite  to 
the  argument  of  I'O. 

If  it  be  desired  to  transform  Tables  5  and  6  into  others  that  shall 
show  the  proportion  of  cases  in  which  the  plus  Errors  and  the  minus 
Errors  respectively  lie  within  various  extreme  limits,  their  entries 
would  have  to  be  halved. 

Let  us  suppose  this  to  have  been  done  to  Table  6,  and  that  a 
new  Table,  which  it  is  not  necessary  to  print,  has  been  thereby  pro- 
duced and  which  we  will  call  6a.  Next  multiply  all  the  entries  in  the 
new  Table  by  100  in  order  to  make  them  refer  to  a  total  number 
of  100  cases,  and  call  this  second  Table  6b.  Lastly  make  a  converse 
Table  to  66 ;  one  in  which  the  arguments  of  6b  become  the  entries, 
and  the  entries  of  6b  become  the  arguments.     From  this  the  Table  7 


202 


NATURAL  INHERITANCE. 


is  made.  For  example,  in  Table  6,  opposite  to  the  argument  TOO,  the 
entry  of  '50  is  found ;  that  entry  becomes  "25  in  6a,  and  25  in  66. 
In  Table  7  the  argument  is  25,  and  the  corresponding  entry  is  1-00. 
The  meaning  of  this  is,  that  in  25  per  cent,  of  the  cases  the  greatest 
of  the  Errors  just  attains  to  ±  1-0.  Similarly  Table  7  shows  that 
the  greatest  of  the  Errors  in  30  per  cent,  of  the  cases,  just  attains 
to  ±  1"25  ;  in  40  per  cent,  to  1*90,  and  so  on.  These  various  per- 
centages correspond  to  the  centesimal  Grades  in  a  Curve  of  Distri- 
bution, when  the  Grade  0°  is  placed  at  the  middle  of  the  axis,  which 
is  the  point  where  it  is  cut  by  the  Curve,  and  where  the  other 
Grades  are  reckoned  outwards  on  either  hand,  up  to  +  50°  on  the 
one  side,  and  to  —  50°  on  the  other. 

To  recapitulate  : — In  order  to  obtain  Table  7  from  the  primary 
Table  5,  we  have  to  halve  each  of  the  entries  in  the  body  of  Table  5, 
then  to  multiply  each  of  the  arguments  by  100,  and  divide  it  by 
°4769.  Then  we  expand  the  Table  by  interpolations,  so  as  to 
include  among  its  entries  every  whole  number  from  1  to  99  inclusive. 
Selecting  these  and  disregarding  the  rest,  we  turn  them  into  the 
arguments  of  Table  7,  and  we  turn  their  corresponding  arguments 
into  the  entries  in  Table  7. 

Table  7. 

Ordina-tes  to  Normal  Curve  of  Distribution 

on  a  scale  whose  unit  =  the  Probable  Error  ;  and  in  which  the  100  Grades  run 
from  0°  to  +  50°  on  the  one  side,  and  to  -  50°  on  the  other. 


Grades. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 

0-00 

0-04 

0-07 

0-11 

0-15 

0.19 

0-22 

0-26 

0-30 

0-34 

10 

0-38 

0-41 

0-45 

0-49 

0-53 

0-57 

0-61 

0-65 

0-69 

0-74 

20 

0-78 

0-82 

0-86 

0-97 

0-95 

1-00 

1*05 

1-10 

1-15 

1-20 

30 

3-25 

1-30 

1-36 

1-42 

1-47 

1-54 

1-60 

1-67 

1-74 

1-82 

40 

1-90 

1-99 

2-08 

2-19 

2-31 

2-44 

2-60 

2-79 

3-05 

3-45 

But  in  the  Schemes,  the  100  Grades  do  not  run  from— 50°  through 
0°  to  +  50°,  but  from  0°  to  100°.  It  is  therefore  convenient  to 
modify  Table  7  in  a  manner  that  will  admit  of  its  being  used 
directly  for  drawing  Schemes  without  troublesome  additions  or 
subtractions.  This  is  done  in  Table  8,  where  the  values  from 
50°  onwards,  and  those  from  50°  backwards  are  identical  with 
those  in  Table  7  from  0°  to  ±  50°,  but  the  first  half  of  those 
in  Table  8   are  positive  and   the  latter  half  are  negative. 


TABLES. 


205 


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206 


NATURAL  INHERITANCE. 


Table  9. 

Marriage  Selection  in  respect  to  Stature. 

The  205  male  parents  and  the  205  female  parents  are  each  divided  into  three 
groups — T,  M,  and  S,  and  t,  m,  and  s,  respectively — that  is.  Tall,  Medium,  and 
Stiort  (medium  male  measurements  being  taken  as  67  inches,  and  upwards  to  70 
inches).  The  number  of  marriages  in  each  possible  combination  between  them 
were  then  counted,  with  the  result  that  men  and  women  of  contrasted  heights, 
Short  and  Tall,  or  Tall  and  Short,  married  about  as  frequently  as  men  and  women 
of  similar  heights,  both  Tall  or  both  Short ;  there  were  32  cases  of  the  one  to 
27  of  the  other. 


s.,  t. 

12  cases. 

M.,  t. 

20  cases. 

T.,  t. 
18  cases. 

S.,  m. 
25  cases. 

M.,  m. 

51  cases. 

T.,  m. 

28  cases. 

S.,  s. 
9  cases. 

M.,  s. 
28  cases. 

T.,  s. 
14  cases. 

Short  and  tall,  12  +  14  =  3 2  cases. 

Short  and  short,  9  \   _  ^,7 

Tall  and  tall,  18     f   -  ^'  ^^a^®^- 

We  may  therefore  regard  the  married  folk  as  couples  picked  out  of  the  general 
population  at  haphazard  when  applying  the  law  of  probabilities  to  heredity  of 
stature. 


Table  9a. 

Marriage  Selection  in  respect  to  Eye- Colour 
in  78  Parental  Couples. 


Eye  Colour  of 

No.  of 

cases 

observed. 

Per  Cents. 

'Eije  Colour 
of  Husband 
and  Wife. 

Husband 

Wife. 

Obs. 

Chance. 

Observed. 

Chance. 

Light 
Hazel 
Dark 

Light 
Hazel 
Dark 

29 
2 
6 

37 
3 

8 

37 
2 

7 

}" 

46 

Alike 

Light 
Hazel 

Hazel 
Dark 

Hazel 
Light 

Dark 
Hazel 

}  - 
1    ^ 

23 
5 

15 

7 

V      28 

22 

/  Half-con- 
\  trasted 

Light 
Dark 

Dark 

Light 

i   " 

24 

32 

24 

32 

Contrasted 

The  chance  combinations  in  pairs  are  calculated  for  a  population  containing 
61*2  per  cent,  of  Light  Eye-colour,  12-7  of  Hazel,  and  26-1  of  Dark. 


TABLES. 


207 


Table  9  b. 

Marriages  of  the  Artistic  and  the  Not  Artistic. 


Rank  in  Pedigrees. 

No.  of 
per- 
sons. 

Percentages. 

Pairs  of  artistic  and  not  artistic 
persons. 

Marriages 
observed. 

Chance 
combinations. 

art. , 

not. 

art. 

not. 

both 
art. 

1  art. 
Inot. 

both 
not. 

both 
art. 

1  art. 
Inot. 

both 
not. 

Parents 

326 

280 

288 

32 

27 
24 

68 
73 

76 

39 
30 

28 

61 

70 

72 

14 

12 

9 

31 
31 
41 

50 
57 
50 

12 

8 

7 

46 
41 
39 

42 
51 
54 

Paternal  grandparents.. 
Maternal  grandparents.. 

Totals  and  means... 

894 

28 

72 

33 

67 

12 

36 

52 

9 

42 

49 

Tastes  of  Husband  and  Wife — alil^'ft  

12  -f  52  =64 
36 

9  +  49  =  58 
42 

( 

3ontrastp.d 

Table    10. 

Effect  upon  Adult  Children  of  Differences  in  Height  of  their 

Parents. 


Difference  in  inches 

between  the  Heights 

of  the  Parents. 

Proportion  per  50  of  cases  in  which 

the  Heights^  of  the  Children 

deviated  to  various  amounts  from 

the  Mid-filial  Stature  of  their 

respective  families. 

Number  of 

Children  whose 

Heights  were 

observed. 

(Total  525. ) 

Less  than 
2  inches. 

^CO 

Cj      (X) 

Under  1  inch 

21 
23 
16 
24 

18 

35 
37 
34 
35 
30 

43 
46 
41 
41 

40 

46 
49 
45 
47 
47 

48 
50 
49 
49 
49 

105 
122 
112 

108 

78 

1  and  under  2    

2  „          3      

3  „          5    , 

5  and  above 

^  Every  female  height  has  been  transmuted  to  its  male  equivalent  by  multi- 
plying it  byl"08,  and  only  those  families  have  been  included  in  which  the 
number  of  adult  children  amounted  to  six,  at  least. 

j^OTE. — When  these  figures  are  protracted  into  curves,  it  will  be  seen — (1) 
that  they  run  much  alike  ;  (2)  that  their  peculiarities  are  not  in  sequence  ;  and 
(3)  that  the  curve  corresponding  to  the  first  line  occupies  a  medium  position.  It 
is  therefore  certain  that  differences  in  the  heigh  ts  of  the  Parents  have  on  the 
whole  an  inconsiderable  effect  on  the  heights  of  their  Offspring. 


208 


NATURAL  INHERITANCE. 


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TABLES. 


209 


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210 


NATURAL  INHERITANCE. 


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TABLES. 


211 


Table  14  (Special  Data). 

Deviations  of  individual  Brothees  from  their  Mid-Fraternal 

Statures. 


Number  of  brothers  in  eacli  family 

4 

5 

6 

7 

Number  of  Families 

39 

23 

8 

6 

Amount  of  Deviation. 

Number 
of  cases. 

Number 
of  cases. 

Number 
of  cases. 

Number 
of  cases. 

Under  1  inch 

88 

49 

15 

4 

62 

30 

17 

3 

3 

20 

18 

5 

3 

2 

21 

14 

6 

1 

1  and  under  2 

2  and  under  3 

3  and  under  4 

4  and  above 

P  2 


212 


NATURAL  INHERITANCE. 


vo  fe 


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OS  05  p  O 

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7—1  i-i 

p 

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p 

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o 
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T-l 

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p 

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p 
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p 

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CM  rtl  -^  r-l 

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t^  ^ti  1^  OS 

t^  CO  CO  00 

7-(    CM    7— 1 

00 

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CM  CO  O  00 

CO  t^  7— 1  J:^ 

7—1    7—1    CM 

CO 
Oi 

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OS  j>.  i>.  j>. 

O  O  tr^  CO 
CO  ^  CO  7-1 

O 
CD 
CM 

7—1 

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7—1    7—1    CO 

CO 

t^  CM  7-1  CO 
CM  CM 

CD 

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CM  -*  XO 

7—1 

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T— 1 

Sex  and  the 
No.  of  the 
(ascending) 
generation. 

HH  1— 1  1— 1  H- 
«3 

Is 

1— < 

1 — 1  >— 1  1— 1  1— 1 

Is 

B 

1^ 

K*  1— 1  H- i    : 

HH  Hi  I—I  l-H 

CO 
CO           r-H 

1 

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TABLES. 


213 


Table    16. 

The  Descent  of  Hazel-eyed  Families. 


Total 
cases. 

Observed. 

Percentages, 

Light. 

Hazel,  Dark, 

Light, 

Hazel. 

Dark. 

General  population    

III.  Grandparents 

11    Parents 

4490 
449 
336 
948 

2746 
267 
165 
430 

569 
61 

85 
302 

1175 
121 

86 
216 

61-2 
60 
49 
45 

12-7 
13 

25 
32 

26^ 
27 
26 
23 

I.  Children 

Table    17. 

Calculated  Contributions  of  Eye-colour. 


Contribution  to  the 
heritage  from  each. 

Data  limited  to  the  eye-colours  of  the 

2  parents. 

4  grandparents. 

2  parents  and 
4  grandparents. 

L 

IL 

in. 

Light. 

Dark. 

Light. 

Dark. 

Light. 

Dark. 

Light-eyed  parent 

0-30 
0-20 

0-28 

0-10 
0-30 

0'12 

0-16 
0-10 

0-25 

■    0-66 
0-16 

0-11 

0-25 
0-16 

0-08 
0-05 

0-12 

0'09 
0-25 

0  -OS 
0-08 

0-06 

Hazel-eyed  parent 

Dark-eyed  parent 

Light-eyed  grandparent.. 
Hazel-eyed  grandparent . 
Dark-eyed  grandparent... 

Residue,      rateably     as- 
signed   

214 


NATURAL  INHERITANCE. 


Table  18. 

Example  of  One  Calculation  in  each  of  the  Theee  Cases. 


Ancestry  and  their 
eye-colours. 


I. 


o 

O 


Light-eyed  parents. 
Hazel-eyed  parents. 
Dark-eyed  parents . 

Light-eyed  grand- 
parents  

Hazel-eyed  grand- 
parents  

Dark-eyed  grand 
parents 


Contribute 
to 


Lisrht. 


Dark. 


0-60 


Residue,  rateably  as- 
signed  


Total  contributions 


0-28 


0-88 


0-12 


0-12 


1-00 


6  '^ 


II. 


Contribute 
to 


Light. 


0-16 
0-20 

0-25 


0-61 


Dark. 


012 
0-16 

0-11 


0-39 


1-00 


o 

O    cS 

d 


III. 


Contribute 
to 


Light. 


016 

0-08 
010 

012 


0-46 


Dark. 


0-09 
0-25 


0-06 
0-08 

0-06 


0-54 


1-00 


TABLES. 


215 


Table  19. 

Obseeved  and  Calculated  Eye-coloues  in  16  Geoups  of  Families. 

Those  families  are  grouped  together  in  whom  the  distribution  of  Light,  Hazel, 
and  Dark  Eye-colour  among  the  Parents  and  Grandparents  is  alike.  Each  group 
contains  at  least  Twenty  Brothers  or  Sisters. 


Eye-colours  of  the 

Total 

Number  of  the  light  eye- 
coloured  children. 

Parents. 

Grandparents. 

child- 

Calculated. 

ren. 

Ob- 
served. 

Light. 

Hazel. 

Dark. 

Light. 

Hazel, 

Dark. 

I. 

II. 

III. 

2 

4 

183 

174 

161 

163 

172 

2 

3 

i 

53 

46 

47 

44 

48 

2 

3 

... 

"i 

92 

88 

81 

67 

79 

2 

2 

i 

1 

27 

26 

24 

18 

22 

... 

2 

2 

2 

22 

11 

6 

12 

6 

3 

i 

62 

52 

48 

51 

51 

3 

"i 

42 

30 

33 

31 

32 

1 

2 

2 

... 

31 

28 

24 

24 

20 

2 

"i 

49 

35 

38 

28 

34 

2 

"i 

1 

31 

25 

24 

21 

23 

3 

1 

76 

45 

44 

55 

46 

2 

. .  • 

2 

66 

30 

38 

38 

35 

2 

1 

27 

15 

16 

18 

16 

1 

... 

3 

20 

9 

12 

8 

9 

1 

i 

2 

22 

8 

13 

11 

11 

"i 

1 

1 

2 

24 

9 

14 

12 

10 

629 

623 

601 

614 

216 


NATURAL  INHERITANCE, 


Table  20, 

Observed  and  Calculated  Eye-Coloues  in   78    separate  Families,  each 

OF   NOT   less   than    SiX   BROTHERS    OR   SiSTERS. 


Eye-colours  of  the 

Number  of  the  light  eye- 

Total 

coloured  children. 

Parents. 

Grandparents. 

child- 
ren. 

Ob- 
served. 

Calculated. 

Light. 

Hazel. 

Dark. 

Light. 

Hazel, 

Dark. 

L 

n. 

III. 

2 

4 

6 

6 

5-3 

5-3 

5-6 

2 

4 

6 

6 

5-3 

5-3 

5-6 

2 

4 

6 

6 

5-3 

5-3 

5-6 

2 

4 

6 

5 

5-3 

5-3 

5-6 

2 

4 

7 

7 

6-2 

6-2 

Q-Q 

2 

4 

7 

7 

6-2 

6-2 

6-6 

2 

4 

7 

7 

6-2 

6-2 

6-6 

2 

4 

7 

7 

6-2 

6-2 

Q-Q 

2 

4 

7 

7 

6-2 

6-2 

Q-Q 

2 

4 

8 

8 

7-0 

7-1 

7-5 

2 

4 

8 

8 

7-0 

7-1 

7-5 

2 

4 

8 

8 

7-0 

7-1 

7-5 

2 

4 

8 

8 

7-0 

7-1 

7-5 

2 

4 

8 

7 

7-0 

7-1 

7-5 

2 

4 

8 

7 

7-0 

7-1 

7-5 

2 

4 

12 

12 

10-6 

10-7 

11-3 

2 

3 

"'i 

7 

7 

6-2 

5-8 

6-4 

2 

3 

1 

10 

4 

8-8 

8-3 

9-1 

2 

3 

1 

12 

12 

10-6 

10-0 

10-9 

2 

3 

1 

'  1 

6 

6-2 

5-1 

6-0 

2 

3 

1 

8 

8 

7-0 

5-8 

6-9 

2 

3 

1 

9 

9 

7-9 

6-6 

7-7 

2 

S 

1 

9 

9 

7-9 

Q-Q 

7-7 

2 

3 

1 

9 

7 

7-9 

^■Q 

7-7 

2 

3 

1 

10 

10 

8-8 

7-3 

8-6 

2 

2 

2 

7 

7 

6-2 

5-4 

6-2 

2 

2 

2 

10 

9 

8-8 

7-7 

8-8 

2 

2 

1 

"i 

6 

6 

5-3 

4-0 

5-0 

2 

2 

1 

1 

10 

10 

8-8 

6-7 

8-3 

2 

2 

1 

1 

7 

4 

6-2 

4-7 

4  6 

2 

2 

2 

8 

5 

5-4 

4-6 

4-8 

2 

3 

1 

6 

2 

1-7 

4-4 

2-2 

2 

2 

2 

9 

1 

2-5 

5-1 

2-5 

2 

1 

3 

6 

1 

2-7 

2-5 

1-2 

2 

1 

3 

11 

3 

3-1 

4-5 

2-2 

2 

1 

2 

6 

1-7 

3-0 

1-5 

2 

1 

2 

7 

4 

2-0 

3-6 

1-8 

.  ■  • 

3 

6 

6 

4-7 

5  0 

4-9 

3 

7 

6 

5-5 

5-7 

5-7 

3 

8 

6 

6-2 

6-6 

%-Q 

3 

9 

7 

7-0 

7-5 

7-4 

3 

11 

10 

8-6 

9-1 

9-2 

TABLES. 

Table  20 — continued. 


217 


Eye-colours  of  the 

Total 

Number  of  the  light  eye- 
coloured  children. 

Parents. 

Grandparents. 

child- 

Childreii 

I. 

ren. 

Ob- 
served. 

Light. 

Hazel, 

De 

irk.    Light. 

Hf 

izel.  Dark. 

I. 

II. 

III. 

1 

1 

3 

1 

9 

6 

7-0 

6 

6 

6-9 

1 

1 

3 

1 

11 

7 

8-6 

8 

0 

8-5 

1 

1 

2 

2 

7 

6 

5-5 

5- 

4 

4-4 

1 

1 

2 

2 

9 

9 

7-0 

"     6 

9 

5-7 

1 

1 

2 

2 

11 

1 

8-6 

8 

5 

6-9 

1 

1 

2 

2 

6 

6 

4-7 

3 

4 

4-1 

1 

2 

2 

6 

4 

4-7 

3 

4 

4-1 

1 

2 

2 

8 

5 

6-2 

4 

6 

5-5 

1 

2 

2 

9 

7 

7-0 

5 

1 

6-2 

1 

2 

1            1 

6 

6 

4-7 

4 

0 

4-4 

1 

2 

1            1 

10 

9 

7-8 

6 

7 

7-4 

1 

1 

3 

9 

4 

7-0 

5 

5 

6-8 

1 

1 

1            2 

8 

5 

6-2 

4 

1 

5-3 

1           4 

7 

3 

4-1 

6 

2 

4-8 

1            3 

i 

6 

4 

3-5 

4 

4 

3-7 

1           3 

1 

7 

3 

41 

5 

1 

4-3 

1            3 

1 

8 

6 

4-6 

5 

8 

4-9 

1            3 

1 

8 

5 

4-6 

.    5 

8 

4-9 

1            3 

1 

8 

4 

4-6 

5 

8 

4-9 

1            3 

1 

9 

6 

5  2 

6 

6 

5-5  . 

1            3 

1 

9 

5 

5-2 

6 

6 

5-5 

1            2 

2 

6 

5 

3-5 

3 

•4 

3-2 

1            2 

2 

6 

3 

3-5 

3 

•4 

3-2 

1            2 

2 

8 

4 

4-6 

4 

•6 

4-2 

1            2 

2 

10 

2 

5-8 

5 

•7 

5-3 

1            2 

2 

14 

9 

8-1 

8 

•0 

7-4 

1            2 

1            1 

7 

5 

4-1 

4 

•7 

4-1 

1            1 

2            1 

7 

3 

4-1 

4 

3 

3-9 

1            1 

1            2 

7 

4 

4-1 

3 

6 

3  5 

1            1 

3 

8 

4 

4-6 

3 

•3 

3-6 

I 

1            1 

3 

8 

3 

4-6 

3 

3 

3-6 

1            3 

6 

3 

3-5 

2 

1 

2-6 

1 

1            2 

2 

6 

3 

4-8 

3 

•4 

2-6 

1 

1            2 

1            1 

9 

4 

7-0 

6 

•0 

4-4 

1 

1            1 

3 

13 

8 

10-1 

5 

•3 

4-7 

... 

1 

4 

7 

2 

5-5 

4-6 

3-4 

218 


NATURAL  INHERITANCE. 


Table    21. 

Error  in  Calculatioxs. 

Numbers  of  Errors  of  various  Amounts  in  the  3  Calculations,  Table  20,  of  the 
Number  of  Light  Eye-coloured  Children  in  the  78  Families. 


Data  employed  referring  to 

Amount  of  Errors. 

Total 

Cases. 

0-0 

to 

0-5. 

0-6 
to 
1-1 

1-2 

to 

1-7 

1-8 

to 

2-3 

2-4 
and 
above. 

I.  The  2  parents  only 

II.  The  4  grandparents  only 

III.   The  2  parents  and  4  grand- 
p  arents 

19 
16 

41 

30 

28 

17 

18 
10 

8 

5 
10 

4 

6 

14 

8 

78 
78 

78 

Table    22. 
Inheritance  of  the  Artistic  Faculty. 


Parents. 

Children. 

Observed. 

Per  cents. 

Number 

of 
Fraterni- 
ties. 

Total 
children. 

Of  whom 

are 
artistic. 

Observed. 

Calculated. 

art. 

not 
art. 

art. 

not 
art. 

Both  artistic 

30 
101 
150 

148 
520 
839 

95 
201 
173 

64 
39 
21 

36 
61 
79 

60 
39 
17 

40 
61 
83 

One  artistic;  one  not.. 
Neither  artistic ... 

Totals 

281 

1507 

469 

100 

100 

100 

100 

The  "parents  "  and  the  "  children  "  in  this  Table  usually  rank  respectively  as 
Grandparents  and  Parents  in  the  E.F.F.  pedigrees. 


APPENDIX. 


The  following  memoirs  by  the  author,  bearing  on  Heredity,  have 
been  variously  utilised  in  this  volume  : 

Experiments  in  Pangenesis.  Proc.  Royal  Soc,  No.  127, 1871,  p.  393, 

Blood  Relationship.  Froc.  Royal  Soc,  No.  136,  1872,  p.  394. 

A  Theory  of  Heredity.     Journ.  Anthropol.  Inst.,  1875,  p.  329. 

Statistics  by  Inter  comparison.    Phil.  Mag.,  Jan.  1875. 

*0n  the  Probability  of  the  Extinction  of  Families.  Journ.  Anthropol. 

Inst.,  1875. 
Typical  laws  of  Heredity.     Journ.  Royal  Inst.,  Feb.  1877. 
^Geometric  Mean  in  Vital  and  Social  Statistics.    Proc.  Royal  Soc, 

No.  198,  1879.     See  subsequent  memoir  by  Dr.  Macalister. 
Address   to    Anthrop.    Section   British    Association    at    Aberdeen. 

Journ.  Brit.  Assoc,  1885. 
Regression  towards    Mediocrity    in    Hereditary    Stature,      Journ. 

Anthropol.  Inst,  1885. 
Presidential  Addresses  to  Anthropol.  Inst.,  1885,  6  and  7. 
Family  Likeness  in  Stature.     Proc  Royal  Soc,  No.  242,  1886. 
Family  Likeness  in  Eye-colour.      Proc   Royal  Soc,  No.  245,  1886. 
*Good  and  Bad  Temper  in  Eoglish  Families.     Fortnightly  Review, 

July,  1887. 
Pedigree    Moth    Breeding.*     Trans.  Entomolog.   Soc,  1887.      See 

also  subsequent  memoir  by  Mr.  Merrifield,  and  another  read 

by  him,  Dec.  1887. 

Those  marked  with   an  asterisk  (*)  are   reprinted  with  slight  revision  in  the 
Appendices  F,  D,  and  E. 


220  NATURAL  INHERITANCE. 

WORKS  ON  HEREDITY  BY  THE  AUTHOR. 

(Published  by  Messrs.  Macmillan  &,  Co.) 

Hereditary  Genius.      1869. 
EDglish  Men  of  Science.     1874. 
Inquiries  into  Human  Faculty.     1883. 


Record  of  Family  Faculties.!     1884.  2s.  Qd. 

Life  History  Album. '^  (edited  byF.  Galton).   1884.  3s.  6d.  and  45.  6d. 

^  The  Eecord  of  Family  Facnl-tieis  consists  ,of  Tabular  Forms  and  Directions 
for  entering  Data,  with  an  Explanatory  Preface.  It  is  a  large  thin  quarto  book 
of  seventy  pages,  bound  in  limp  cloth.  The  first  part  of  it  contains  a  preface, 
with  explanation  of  the  object  of  the  work  and  of  the  way  in  which  it  is  to  be 
used.  The  rest  consists  of  blank  forms,  with  printed  questions  and  blank  spaces  to 
be  :^l!ed  withj\Titing.  The  Record  is  designed  to  facilitate  the  orderly  collection  of 
such  data  as  are  important  to  a  family  from  an  hereditably  point  of  view.  It  allots 
equal  space  to  everj^  direct  ancestor  in  the  nearer  degrees,  and  is  supposed  to  be  filled 
up  in  most  cases  by  a  parent,  say  the  father  of  a  growing  family.  If  he  takes 
pains  to  make  inquiries  of  elderly  relatives  and  friends,  and  to  seek  in  registers, 
he  will  be  able  to  ascertain  most  of  the  required  particulars  concerning  not  only 
his  own  parents,  but  also  concerning  his  four  grandparents  ;  and  he  can  ascertain 
like  particulars  concerning  those  of  his  wife.  Therefore  his  children  will  be  pro- 
vided with  a  large  store  of  information  about  their  two  parents,  four  grandparents, 
and  eight  great-grandparents,  which  form  the  whole  of  their  fourteen  nearest 
ancestors.  A  separate  schedule  is  allotted  to  each  of  them.  Space  is  afterwards 
provided  for  the  more  important  data  concerning  many  at  least,  of  the  brothers 
and  sisters  of  each  direct  ancestor.  The  schedules  are  followed  by  Summary 
Tables,  in  which  the  distribution  of  any  characteristic  throughout  the  family  at 
large  may  be  compendiously  exhibited. 

^  The  Life  History  Album  was  prepared  by  a  Sub-Committee  of  the  Collective 
Investigation  Committee  of  the  British  Medical  Association.  It  is  designed  to 
serve  as  a  continuous  register  of  the  principal  biological  facts  in  the  life  of  its 
owner.  The  book  begins  with  a  few  pages  of  explanatory  remarks,  followed  by 
tables  and  charts.  The  first  table  is  to  contain  a  brief  medical  historj^  of  each 
member  of  the  near  ancestry  of  the  owaier.  This  is  followed  by  printed  forms 
on  which  the  main  facts  of  the  owner's  growth  and  development  from  birth 
onwards  may  be  registered,  and  by  charts  on  winch  measurements  may  be  laid 
down  at  appropriate  intervals  and  compared  with  the  curves  of  normal  growth. 
Most  of  the  required  data  are  such  as  any  intelligent  person  is  capable  of  record- 
ing ;  those  that  refer  to  illnesses  should  be  brief  and  technical,  and  ought  to  be 
filled  up  by  the  medical  attendant.  Explanations  are  given  of  the  most  'con- 
venient tests  of  muscular  force,  of  keenness  of  eyesight  and  hearing,  and  of  the 
colour  sense.  The  4.s.  6d.  edition  contains  a  card  of  variously  coloured  wools  to 
test  the  sense  of  colour. 

*)f."^  These  two  works  pursue  similar  objects  of  personal  and  scientific  utility, 
along  different  paths.     The  Album  is  designed  to  lay  the  foundation  of  a  practice 


APPENDIX  B.  221 

of  maintaining  tmslworthy  life-Mstories  that  shall  be  of  medical  service  in  after- 
life to  the  person  who  keeps  them.  The  Record  shows  how  the  life  histories  of 
members  of  the  same  family  may  be  collated  and  used  to  forecast  the  development 
in  mind  and  body  of  the  younger  generation  of  that  family.  Both  works  are 
intended  to  promote  the  registration  of  a  large  amount  of  information  that  has 
hitherto  been  allowed  to  run  to  waste  in  oblivion,  instead  of  accumulating  and 
forming  stores  of  recorded  experience  for  future  personal  use,  and  from  which 
future  inquirers  into  heredity  may  hope  to  draw  copious  supplies. 


B. 


PROBLEMS    BY   J.    D.    HAMILTON    DICKSONj    FELLOW   AND    TUTOR   OF 

ST.  Peter's  college,  Cambridge. 

{Reprinted  from  Proc.  Royal  S'oc,  No.  242,  1886,  p.  63.) 

Prohlem  1. — A  point  P  is  capable  o£  moving  along  a  straight  line 
P'OP,  making  an  angle  tan~i|  ^ith  the  a2:is  of  y,  which  is  drawn 
through  O  the  mean  position  of  P ;  the  probable  error  of  the  pro- 
jection of  P  on  Oy  is  1*22  inch  :  another  point  jt?,  whose  mean  posi- 
tion at  any  time  is  P,  is  capable  of  moving  from  P  parallel  to  the 
axis  of  X  (rectangular  co-ordinates)  with  a  probable  error  of 
1'50  inch.     To  discuss  the  "surface  of  frequency"  of  p. 

1.  Expressing  the  "  surface  of  frequency "  by  an  equation  in 
X,  y,  z,  tbe  exponent,  with  its  sign  changed,  of  the  exponential 
which  appears  in  the  value  of  z  in  the  equation  of  the  surface  is, 
save  as  to  a  factor, 

y^      ^  (3^'-2y)2      ,     .     .     ^     ^  /2) 


(1-22)2        9(1-50)2 

hence  all  sections  of  the  "  surface  of  frequency  "  by  planes  parallel 
to  the  plane  of  xy  are  ellipses,  whose  equations  may  be  written  in 
the  form, 

2.   Tangents  to  these  ellipses  parallel  to  the  axis  of  7/ are  found, 


222 


NATURAL  INHERITANCE. 


by  differentiatiDg  (2)  and  putting  the  coefficient  of  dy  equal  to  zero, 
to  meet  the  ellipses  on  the  line, 


(1-22)^ 


^  3a?-22/_^ 
"9(1-50)2       ' 


6 


that  is 


y_^      9(i-5oy 

X 


1 


+ 


17-6 


(3) 


(1-22)2     9(1-50)^ 


X.     Let  this  be  the  line  OM. 


or,  approximately,  on  the  line  y  - 
(See  Fig.  11,  p.   101.) 

From  the  nature  of  conjugate  diameters,  and  because  P  is  the 
mean  position  of  p,  it  is  evident  that  tangents  to  these  ellipses 
parallel  to  the  axis  of  x  meet  them  on  the  line  x  =  §?/,  viz.,  on  OP. 

3.  Sections  of  the  ''  surface  of  frequency  "  parallel  to  the  plane 
of  xz^  are,  from  the  nature  of  the  question,  evidently  curves  of  fre- 
quency with  a  probable  error  1  -50,  and  the  locus  of  their  vertices 
lies  in  the  plane  z  OP. 

Sections  of  the  same  surface  parallel  to  the  plane  of  yz  are  got 
from  the  exponential  factor  (1)  by  making  £c  constant.  The  result  is 
simplified  by  taking  the  origui  on  the  line  OM.  Thus  putting  x^=.  x^ 
and  y  =  yi  +  y',  where  by  (3) 


(1-22)2  9(1-50)2 


0 


the  exponential  takes  the  form 
1.4) 


{ 


+  ■ 


■y''  + 


f    .vi^    A^^i-W 


+ 


(1-22)2   ■  9(1-50)2)  "^     '    ((1-22)2         9(l-50;2 
whence,  if  e  be  the  probable  error  of  this  section, 

i  1.4 

72 


} 


(4) 


+ 


(5) 


(1-22)2       9(1-50)2 

or    Ton   referring   to    (3)1    e  =  1-50        / 

that  is,  the  probable  error  of  sections  parallel  to  the  plane  of  yz  is 
nearly  —y=-  times  that  of  those  parallel  to  the  plane  of  xz,  and  the 
locus  of  their  vertices  lies  in  the  plane  ^iOM. 


APPENDIX  B.  223 

It  is  important  to  notice  that  all  sections  parallel  to  the  same 
co-ordinate  plane  have  the  same  probable  error. 

4.  The  ellipses  (2)  when  referred  to  their  principal  axes  become, 
after  some  arithmetical  simplification, 

/2  '2 

+  -^ —  =  constant, (6) 

20-68      5-92  '  ^  ' 

the  major  axis  being  inclined  to  the  axis  of  x  at  an  angle  whose 
tangent   is    0"5014.      [In   the    approximate    case   the   ellipses    are 

—  +  -^^—  =  const.,  and  the  maior  axis  is  inclined  to  the  axis  of  x  at 

7         2  -■ 

an  angle  tan~"ii.] 

5.  The  question  may  be  solved  in  general  terms  by  putting 
YON  =  ^,  XOM  =  ^,  and  replacing  the  probable  errors  1*22  and 
1*50  by  a  and  h  respectively;  then  the  ellipses  (2)  are, 

^  ^  (x  -  y  tan  Of  ^  ^ .^. 

equation  (3)  becomes 

2/^,4-       n^-V  tan  0       /-. 

V      ,        ,  o?-  tan  B        C   '     '     '     '     '     \  ) 

or  -   =  tan  <p  =  — -— 

X  0^  +  a'^  tan^^ 

and  (5)  becomes  — _,=—-  +  -— — (9) 

whence  %  =— „ (10) 

tan  0      h^  ^     ^ 

If  G  be  'the  probable  error  of  the  projection  of  ^^'s  whole  motion 
on  the  plane  of  xz,  then 

c^  =  a^  tan^  6  +  Ij^, 

which  is  independent  of  the  distance  of  ^'s  line  of  motion  from  the 

axis  of  X.     Hence  also 

tan  4>  _ci^  /-1 1  \ 

t^^^~~¥ ^     ^ 

Prohlem  2. — An  index  q  moves  under  some  restraint  up  and  down 
a  bar  AQB,  its  mean  position  for  any  given  position  of  the  bar 


224  NATURAL  INHERITANCE. 

being  Q  ;  the  bar,  always  carrying  tbe  index  with  it,  moves  under 
some  restraint  up  and  down  a  fixed  frame  YMY',  the  mean  position 
of  Q  being  M  :  the  movements  of  the  index  relatively  to  the  bar 
and  of  the  bar  relatively  to  the  frame  being  quite  independent.  For 
any  given  observed  position  of  q,  required  the  most  probable  position 
of  Q  fwhich  cannot  be  observed) ;  it  being  known  that  the  probable 
error  of  q  relatively  to  Q  in  all  positions  is  h,  and  that  of  Q  rela- 
tively to  M  is  G.     The  ordinary  law  of  error  is  to  be  assumed. 

If  in  any  one  observation,  MQ  =  x,  Q,q  =  y^  then  the  law  of  error 
requires 


^  +  r (12) 

to  be  a  minimum,  subject  to  the  condition 

X  +  y  =  a,  2^  constant. 
Hence  we  have  at  once,  to  determine  the  most  probable  values  of 

and  the  most  probable  position  of  Q,  measured  from  M,  when  ^'s  ob- 
served distance  from  M  is  a,  is 

h^  +  c2  ""' 

It  also  follows  at  once  that  the  probable  error  i?  of  Q  (which  may 
be  obtained  by  substituting  a—xiovy  in  (12))  is  given  by 

11,1  ^« 

V^        G^        0^  V62_j_c2  ^       ^ 

which  it  is  important  to  notice,  is  the  same  for  all  values  of  a. 


APPENDIX  C. 


223 


C. 


EXPERIMENTS    ON    SWEET    PEAS    BEARING    ON    THE    LAW    OF    REGRESSION. 

The  reason  why  Sweet  Peas  were  chosen,  and  the  methods  of 
selectiug  and  planting  them  are  described  in  Chapter  YI.,  p.  79.  The 
following  Table  justifies  their  selection  by  the  convenient  and  accu- 
rate method  of  weighing,  as  equivalent  to  that  of  measuring  them. 
It  will  be  seen  that  within  the  limits  of  observed  variation  a 
difference  of  0*172  grain  in  weight  corresponds  closely  to  an  average 
difference  of  O'Ol  inch  in  diameter. 


Table  1. 

Comparison  of  Weights  of  Sweet  Peas  with  their  Diameters. 


Distinguishing 
letter  of 

"Weight  of  one 
seed  in  grains. 

Length  of  row  of 
100  seeds  in 

Diameter  of  one 

seed  in  hundredths 

of  inch. 

seed. 

Common  difference 
=  0'172  grain. 

inches. 

Common  difference 
=  0  01  inch. 

K 

1-750 

21-0 

21 

L 

1-578 

20-2 

20 

M 

1-406 

19-2 

19 

N 

r234 

17-9 

18 

0 

1-062 

17-0 

17 

P 

•890 

16-1 

16 

Q 

•718 

15-2 

15 

The  results  of  the  experiment  are  given  in  Table  2  ;  its  first  and 
last  columns  are  those  that  especially  interest  us ;  the  remaining 
columns  showiog  how  these  two  were  obtained. 

It  will  be  seen  that  for  each  increase  of  one  unit  on  the  part  of 
the  parent  seed,  there  is  a  mean  increase  of  only  one-third  of  a  unit 
in  the  filial  seed ;  and  again  that  the  mean  filial  seed  resembles  the 
parental  when  the  latter  is  about  15*5  hundredths  of  an  inch  in 
diameter.  Taking  15-5  as  the  point  towards  which  Filial  Hegression 
points,  whatever  may  be  the  parental  deviation  from  that  point,  the 
mean  Filial  Deviation  will  be  in  the  same  direction,  but  only  one- 
third  as  much. 

Q 


226  NATURAL  INHERITANCE. 

Table  2. 

Parent  Seeds  and  their  Produce. 

Tlie  proportionate  number  of  sweet  peas  of  diififerent  sizes,  produced  by  parent 
seeds  also  of  different  sizes,  are  given  below.  The  measurements  are  those  ot 
their  mean  diameters,  in  hundredths  of  an  inch. 


Diameter 
of  Parent 

Diameters  of  Filial  Seeds. 

Total. 

Mean  Diameter 
of  Filial  Seeds. 

Seed. 

Under 
15. 

15- 

16- 

17- 

18- 

19- 

20- 

Above 
21- 

Observed 

Smoothed 

21 

22 

8 

10 

18 

21 

13' 

6 

2 

100 

17-5 

17-3 

20 

23 

10 

12 

17 

20 

13 

3 

2 

100 

17-3 

17-0 

19 

35 

16 

12 

13 

11 

10 

2 

1 

100 

16-0 

16  6 

IS 

34 

12 

13 

17 

16 

6 

2 

0 

100 

16-3 

16-3 

17 

37 

16 

13 

16 

13 

4 

1 

0 

100 

15-6 

16-0 

16 

34 

15 

18 

16 

13 

3 

1 

0 

100 

16-0 

15-7 

15 

46 

14 

9 

11 

14 

4 

2 

0 

100 

15-3 

15-4 

This  point  is  so  low  in  the  scale,  that  I  possess  less  evidence  than  I 
desired  to  prove  the  bettering  of  the  produce  of  very  small  seeds. 
The  seeds  smaller  than  Q  were  such  a  miserable  set  that  I  could 
hardly  deal  with  them.  Moreover,  they  were  very  infertile.  It  did, 
however,  happen  that  in  a  few  of  the  sets  some  of  the  Q  seeds 
turned  out  very  well. 

If  I  desired  to  lay  much  stress  on  these  experiments,  I  could  make 
my  case  considerably  stronger  by  going  minutely  into  other  details, 
including  confirmatory  measurements  of  the  foliage  and  length  of 
pod,  but  I  do  not  care  to  do  so. 


D. 


GOOD    AND    BAD    TEMPER    IN    ENGLISH    FAMILIES. 


One  of  the  questions  put  to  the  compilers  of  the  Family  Records 
spoken  of  in  page  72,  referred  to  the  "Character  and  Tempera- 
ment "   of  the  persons  described.     These  were  distributed  through 

^  Eeprinted  after  slight  revision  from  FortnigMly  R&view,  July,  1887. 


APPENDIX  D.  227 

three  and  sometimes  four  generations,  and  consisted  of  those  who 
lay  in  the  main  line  of  descent,  together  with  their  brothers 
and  sisters. 

Among  the  replies,  I  find  that  much  information  has  been 
incidentally  included  concerning  what  is  familiarly  called  the 
"temper"  of  no  less  than  1,981  persons.  As  this  is  an  adequate 
number  to  allow  for  many  inductions,  and  as  temper  is  a  strongly 
marked  characteristic  in  all  animals ;  and  again,  as  it  is  of  social 
interest  from  the  large  part  it  plays  in  influencing  domestic  hap- 
piness for  good  or  ill,  it  seemed  a  proper  subject  for  investigation. 

The  best  explanation  of  what  I  myself  mean  by  the  word 
"  temper"  will  be  inferred  from  a  list  of  the  various  epithets  used 
by  the  compilers  of  the  Kecords,  which  I  have  interpreted  as 
expressing  one  or  other  of  its  qualities  or  degrees.  The  epithets 
are  as  follows,  arranged  alphabetically  in  the  two  main  divisions 
of  good  and  bad  temper  : — 

Good  temjjer. — Amiable,  buoyant,  calm,  cool,  equable,  forbearing, 
gentle,  good,  mild,  placid,  self-controlled,  submissive,  sunny,  timid, 
yielding.     (15  epithets  in  all.) 

Bad  tem^oer. — Acrimonious,  aggressive,  arbitrary,  bickering, 
capricious,  captious,  choleric,  contentious,  crotchety,  decisive,  de- 
spotic, domineering,  easily  offended,  fiery,  fits  of  anger,  gloomy, 
grumpy,  harsh,  hasty,  headstrong,  huffy,  impatient,  imperative,  im- 
petuous, insane  temper,  irritable,  morose,  nagging,  obstinate,  odd- 
tempered,  passionate,  peevish,  peppery,  proud,  pugnacious,  quarrel- 
some, quick-tempered,  scolding,  short,  sharp,  sulky,  sullen,  surly, 
uncertain,  vicious,  vindictive.     (46  epithets  in  all.) 

I  also  grouped  the  epithets  as  well  as  I  could,  into  the  following 
five  classes  :   1,  mild  ;  2,  docile  ;  3,  fretful ;  4,  violent ;  5,  masterful. 

Though  the  number  of  epithets  denoting  the  various  kinds  of 
bad  temper  is  three  times  as  large  as  that  used  for  the  good,  yet 
the  number  of  persons  described  under  the  one  general  head  is  about 
the  same  as  that  described  under  the  other.  The  first  set  of  data 
that  I  tried,  gave  the  proportion  of  the  good  to  the  bad-tempered  as 
48  to  52  ;  the  second  set  as  47  to  53.  There  is  little  difference 
between  the  two  sexes  in  the  frequency  of  good  and  bad  temper,  but 
that  little  is  in  favour  of  the  women,  since  about  45  men  are  re- 

2  Q 


228  NATURAL  INHERITANCE. 

corded  as  good-tempered  for  every  55  wlio  are  bad,  and  conversely 
55  women  as  good-tempered  for  45  who  are  bad. 

I  will  not  dwell  on  the  immense  amount  of  unhappiness,  ranging 
from  family  discomfort  down  to  absolute  misery,  or  on  the  breaches 
of  friendship  that  must  have  been  occasioned  by  the  cross-grained, 
sour,  and  savage  dispositions  of  tho^e  who  are  justly  labelled  by 
some  of  the  severer  epithets  ;  or  on  the  comfort,  peace,  and  good- 
will diffused  through  domestic  circles  by  those  who  are  rightly 
described  by  many  of  the  epithets  in  the  first  group.  We  can 
hardly,  too,  help  speculating  uneasily  upon  the  terms  that  our  own 
relatives  would  select  as  most  appropriate  to  our  particular  selves. 
But  these  considerations,  interesting  as  they  are  in  themselves,  lie 
altogether  outside  the  special  purpose  of  this  inquiry. 

In  order  to  ascertain  the  facts  of  which  the  above  statistics  are  a 
brief  summary,  I  began  by  selecting  the  larger  families  out  of  my 
lists,  namely,  those  that  consisted  of  not  less  than  four  brothers  or 
sisters,  and  by  noting  the  persons  they  included  who  were  described 
as  good  or  bad-tempered ;  also  the  remainder  about  whose  temper 
nothing  was  said  either  one  way  or  the  other,  and  whom  perforce  I 
must  call  neutral.  I  am  at  the  same  time  well  aware  that,  in  some 
few  cases  a  tacit  refusal  to  describe  the  ^temper  should  be  inter- 
preted as  reticence  in  respect  to  what  it  was  thought  undesirable 
even  to  touch  upon. 

I  found  that  out  of  a  total  of  1,361  children,  321  were  described 
as  good-tempered,  705  were  not  described  at  all,  and  342  were 
described  as  bad-tempered.  These  numbers  are  nearly  in  the  pro- 
portion of  1,  2,  and  1,  that  is  to  say,  the  good  are  equal  in  number 
to  the  bad-tempered,  and  the  neutral  are  just  as  numerous  as  the 
good  and  bad-tempered  combined. 

The  equality  in  the  total  records  of  good  and  bad  tempers  is  an 
emphatic  testimony  to  the  correct  judgments  of  the  compilers  in  the 
choice  of  their  epithets,  for  whenever  a  group  has  to  be  divided  into 
three  classes,  of  which  the  second  is  called  neutral,  or  medium,  or 
any  other  equivalent  term,  its  nomenclature  demands  that  it  should 
occupy  a  strictly  middlemost  position,  an  equal  number  of  con- 
trasted cases  flanking  it  on  either  hand.  If  more  cases  were 
recorded  of  good  temper  than  of  bad,  the  compilers  would  have  laid 
down  the  boundaries  of   the  neutral  zone  unsymmetrically,  too  far 


APPENDIX  D.  229 

from  the  good  end  of  the  scale  of  temper,  and  too  near  the  bad  end. 
If  the  number  of  cases  of  bad  temper  exceeded  that  of  the  good,  the 
error  would  have  been  in  the  opposite  direction.  But  it  appears,  on 
the  whole,  that  the  compilers  of  the  records  have  erred  neither  to 
the  right  hand  nor  to  the  left.  So  far,  therefore,  their  judgments 
are  shown  to  be  correct. 

ISText  as  regards  the  proportion  between  the  number  of  those  who 
rank  as  neutrals  to  that  of  the  good  or  of  the  bad.  It  was  recorded 
as  2  to  1  ;  is  that  the  proper  poportion  1  Whenever  the  nomencla- 
ture is  obliged  to  be  somewhat  arbitrary,  a  doubtful  term  should  be 
interpreted  in  the  sense  that  may  have  the  widest  suitability.  Now 
a  large  class  of  cases  exist  in  which  the  interpretation  of  the  word 
neutral  is  fixed.  It  is  that  in  which  the  three  grades  of  magnitude 
are  conceived  to  result  from  the  various  possible  combinations  of 
two  elements,  one  of  which  is  positive  and  the  other  negative,  such 
as  good  and  bad,  and  which  are  supposed  to  occur  on  each  occasion 
at  haphazard,  but  in  the  long  run  with  equal  frequency.  The 
number  of  possible  combinations  of  the  two  elements  is  only  four, 
and  each  of  these  must  also  in  the  long  run  occur  with  equal 
frequency.  They  are:  1,  both  positive;  2,  the  first  positive,  the 
second  negative  ;  3,  the  first  negative,  the  second  positive  ;  4,  both 
negative.  In  the  second  and  third  of  these  combinations  the 
negative  counterbalances  the  positive,  and  the  result  is  neutral. 
Therefore  the  proportions  in  which  the  several  events  of  good, 
neutral,  and  bad  would  occur  is  as  1,  2,  and  1.  These  proportions 
further  commend  themselves  on  the  ground  that  the  whole  body  of 
cases  is  thereby  divided  into  two  main  groups,  equal  in  number,  one 
of  which  includes  all  neutral  or  medium  cases,  and  the  other  all 
that  are  exceptional.  Probably  it  was  this  latter  view  that  was 
taken,  it  ma,y  be  half  unconsciously,  by  the  compilers  of  the  Eecords. 
Anyhow,  their  entries  conform  excellently  to  the  proportions  speci- 
fied, and  I  give  them  credit  for  their  practical  appreciation  of  what 
seems  theoretically  to  be  the  fittest  standard.  I  speak,  of  course, 
of  the  Records  taken  as  a  whole  ;  in  small  groups  of  cases  the 
proportion  of  the  neutral  to  the  rest  is  not  so  regular. 

The  results  shown  in  Table  I.  are  obtained  from  all  my  returns. 
It  is  instructive  in  many  ways,  and  not  least  in  showing  to  a 
statistical  eye  how  much  and  how  little  value  may  reasonably  be 


230 


NATURAL  INHERITANCE. 


attached  to  my  materials.  It  was  primarily  intended  to  discover 
whether  any  strong  bias  existed  among  the  compilers  to  spare  the 
characters  of  their  nearest  relatives.  In  not  a  few  cases  they  have 
written  to  me,  saying  that  their  records  had  been  drawn  up  with 
perfect  frankness,  and  earnestly  reminding  me  of  the  importance  of 
not  allowing  their  remarks  to  come  to  the  knowledge  of  the  persons 
described.  It  is  almost  needless  to  repeat  what  I  have  published 
miore  than  once  already,  that  I  treat  the  Records  quite  confidentially. 
I  have  left  written  instructions  that  in  case  of  my  death  they  should 
all  be  destroyed  unread,  except  where  I  have  left  a  note  to  say  that 
the  compiler  wished  them  returned.  In  some  instances  I  know  that 
the  Records  were  compiled  by  a  sort  of  family  council,  one  of  its 
members  acting  as  secretary ;  but  I  doubt  much  whether  it  often 
happened  that  the  Records  were  known  to  many  of  the  members  of 
the  family  in  their  complete  form.  Bearing  these  and  other  con- 
siderations in  mind,  I  thought  the  best  test  for  bias  would  be 
to  divide  the  entries  into  two  contrasted  groups,  one  including 
those  who  figured  in  the  pedigrees  as  either  father,  mother,  son,  or 
daughter— that  is  to  say,  the  compiler  and  those  who  were  very 
nearly  related  to  him — and  the  other  including  the  uncles  and 
aunts  on  both  sides. 

Table  1. 

Distribution  of  Temper  in  Families  (per  cents.) 


Relationships. 

3 

r-H 

o 

o 

ft 

1 

CD 
CO 

1 — 1 

o 

m 

O 

CO 

o  t 

O     CQ 

a.  Fathers  and  Sons  

&.  Mothers  and  Daughters 

c.  Uncles 

d.  Aunts 

a  +  b.   Direct  line 

35 
39 
32 
39 

74 
71 

12 
18 
13 
14 
30 
27 

32 
31 
25 
29 
63 
54 

12 
8 

18 
9 

20 

27 

9 

4 

12 

9 

13 

21 

100 
100 
100 
100 
200 
200 

188 
179 
272 
238 
367 
510 

c  +  d.  Collaterals 

Good. 

Bad  Temper. 

200 
200 

367 
510 

a  +  b.  Dhect  line 

10^ 

Qfi 

c  +  d.  Collaterals 

9 

8 

102 

APPENDIX  D. 


231 


On  compariDg  the  entries,  especially  tlie  summaries  in  the  lower 
lines  of  the  Table,  it  does  not  seem  that  the  characters  of  near 
relatives  are  treated  much  more  tenderly  than  those  of  the  more 
remote.  There  is  little  indication  of  the  compilers  having  been 
biased  by  affection,  respect,  or  fear.  More  cases  of  a  record  being 
left  blank  when  a  bad  temper  ought  to  have  been  recorded,  would 
probably  occur  in  the  direct  line,  but  I  do  not  see  how  this  could  be 
tested.  An  omission  may  be  due  to  pure  ignorance  ;  indeed  I  find 
it  not  uncommon  for  compilers  to  know  very  little  of  some  of  their 
uncles  or  aunts.  The  Records  seem  to  be  serious  and  careful  com- 
positions, hardly  ever  used  as  vehicles  for  personal  animosity,  but 
written  in  much  the  same  fair  frame  of  mind  that  most  people  force 
themselves  into  when  they  write  their  wills. 


Table  2. 
Combinations  of  Temper  in  Marriage  (per  cents.). 


Tempers 
of  Husbands. 

A. — Observed  Pairs. 

B. — Haphazard  Pairs. 

Tempers  of  Wives. 

Tempers  of  Wives. 

Good. 

Bad  Tempers. 

Good. 

Bad  Tempers, 

1 

2 

3 

4 

5 

2 

2 
1 
1 

1 

13 
5 

11 

6 
4 

2 

3 

4 

5 

Good     1 

„        2 

6 
4 

10 

2 

9 
5 

6 

2 

5 

2 

10 
4 

3 
1 

2 
1 

2 
1 
1 

Bad       3 

„        4 

„        5 

14 

7 
3 

4 
3 

9 
3 

2 

3 

2 

5 
2 
2 

8 
5 
3 

2 
1 
1 

Good 

22 

24 

25 

21 

Bad 

3 

1 

23 

3 

0 

24 

The  sexes  are  separated  in  the  Table,  to  show  the  distribution  of 
the  five  classes  of  temper  among  them  severally.  There  is  a  large 
proportion  of  the  violent  and  masterful  among  the  men,  of  the 
fretful,  the  mild,  and  the  docile  among  the  women.  On  adding 
the  entries  it  will  be  found  that  the  proportion  of  those  who  fall 


232  NATURAL  INHERITANCE. 

within  the  several  classes  are  36  per  cent,  of  mild-tempered,  15  per 
cent,  of  docile,  29  per  cent,  of  fretful,  12  per  cent  of  violent,  8  per 
cent,  of  masterful. 

The  importance  assigned  in  marriage-selection  to  good  and  bad 
temper  is  an  interesting  question,  not  only  from  its  bearing  on 
domestic  happiness,  but  also  from  the  influence  it  may  have  in 
promoting  or  retarding  the  natural  good  temper  of  our  race,  assum- 
ing, as  we  may  do  for  the  moment,  that  temper  is  hereditary.  I 
caDnot  deal  with  the~ question  directly,  but  will  give  some  curious  facts 
in  Table  II.  that  throw  indirect  light  upon  it.  There  a  comparison 
is  made  of  (A)  the  actual  frequency  of  marriage  between  persons, 
each  of  the  various  classes  of  temper,  with  (B)  the  calculated  fre- 
quency according  to  the  laws  of  chance,  on  the  supposition  that 
there  had  been  no  marriage-selection  at  all,  but  that  the  pairings, 
so  far  as  temper  is  concerned,  had  been  purely  at  haphazard.  There 
are  only  111  marriages  in  my  lists  in  which  the  tempers  of  both 
parents  are  recorded.  On  the  other  hand,  the  number  of  possible 
combinations  in  couples  of  persons  who  belong  to  the  five  classes  of 
temper  is  very  large,  so  I  make  the  two  groups  comparable  by 
reducing  both  to  percentages. 

It  will  be  seen  that  with  two  apparent  exceptions  in  the  upper 
left-hand  corners  of  either  Table  (of  6  against  13,  and  of  10  against 
5),  there  are  no  indications  of  predilection  for,  or  avoidance  of 
marriage  between  persons  of  any  of  the  five  classes,  but  that  the 
figures  taken  from  observation  run  as  closely  with  those  derived 
through  calculation,  as  could  be  expected  from  the  small  number  of 
observations.  The  apparent  exceptions  are  that  the  percentage  of 
mild-tempered  men  who  marry  mild-tempered  women  is  only  6,  as 
against  13  calculated  by  the  laws  of  chance,  and  that  those  who 
marry  docile  wives  are  1 0,  as  against  a  calculated  5.  There  is  little 
difference  between  mildness  and  docility,  so  we  may  throw  these 
entries  together  without  much  error,  and  then  we  have  6  and  10, 
or  16,  as  against  13  and  5,  or  18,  which  is  a  close  approximation. 
We  may  compare  the  frequency  of  marriages  between  persons 
of  like  temper  in  each  of  the  five  classes  by  reading  the  Table 
diagonally.  They  are  as  (6),  2,  9,  2,  1,  in  the  observed  cases, 
against  (13),  2,  8,  1,  1,  in  the  calculated  ones;  here  the  irregularity 
of  the  6  and  13,  which  are  put  in  brackets  for  distinction  sake,  is 


APPENDIX  D.  233 

conspicuous.  Elsewhere  there  is  not  the  slightest  indication  of  a 
dislike  in  persons  of  similar  tempers,  whether  mild,  docile,  fretful, 
violent,  or  masterful,  to  marry  one  another.  The  large  initial 
figures  6  and  13  catch  the  eye,  and  at  a  first  glance  impress  them- 
selves unduly  on  the  imagination,  and  might  lead  to  erroneous 
speculations  about  mild  tempered  persons,  perhaps  that  they  find  one 
another  rather  insipid  ;  but  the  reasons  I  have  given,  show  conclu- 
sively that  the  recorded  rarity  of  the  marriages  between  mild-tempered 
persons  is  only  apparent.  Lastly,  if  we  disregard  the  five  smaller 
classes  and  attend  only  to  the  main  divisions  of  good  and  bad 
temper,  there  does  not  appear  to  be  much  bias  for,  or  against,  the 
marriage  of  good  or  bad-tempered  persons  in  their  own  or  into  the 
opposite  division. 

The  admixture  of  different  tempers  among  the  brothers  and 
sisters  of  the  same  family  is  a  notable  fact,  due  to  various  causes 
which  act  in  different  directions.  It  is  best  to  consider  them  before 
we  proceed  to  collect  evidence  and  attempt  its  interpretation.  It 
becomes  clear  enough,  and  may  be  now  taken  for  granted,  that  the 
tempers  of  progenitors  do  not  readily  blend  in  the  offspring,  but 
that  some  of  the  children  take  mainly  after  one  of  them,  some  after 
another,  but  with  a  few  threads,  as  it  w^ere,  of  various  ancestral 
tempers  woven  in,  which  occasionally  manifest  themselves.  If  no 
other  influences  intervened,  the  tempers  of  the  children  in  the  same 
family  would  on  this  account  be  almost  as  varied  as  those  of  their 
ancestors ;  and  these,  as  we  have  just  seen,  married  at  haphazard, 
so  far  as  their  tempers  were  concerned  ;  therefore  the  numbers  of 
good  and  bad  children  in  families  would  be  regulated  by  the  same 
laws  of  chance  that  apply  to  a  gambling  table.  But  there  are  other 
influences  to  be  considered.  There  is  a  well-known  tendency  to 
family  likeness  among  brothers  and  sisters,  which  is  due,  not  to 
the  blending  of  ancestral  peculiarities,  but  to  the  prepotence  of  one 
of  the  progenitors,  who  stamped  more  than  his  or  her  fair  share  of 
qualities  u.pon  the  descendants.  It  may  be  due  also  to  a  familiar 
occurrence  that  deserves  but  has  not  yet  received  a  distinctive  name, 
namely,  where  all  the  children  are  alike  and  yet  their  common 
likeness  cannot  be  traced  to  their  progenitors.  A  new  variety  has 
come  into  existence  through  a  process  that  affects  the  whole  Frater- 
nity and  may  result  in  an  unusually  stable  variety  (see  Chapter  III.). 
The  most  strongly  marked  family  type  that  I  have  personally  met 


234  NATURAL  INHERITANCE. 

with,  first  arose  simultaneously  in  the  three  brothers  of  a  family 
who  transmitted  their  peculiarities  with  unusual  tenacity  to  numer- 
ous descendants  through  at  least  four  generations.  Other  influences 
act  in  antagonism  to  the  foregoing ;  they  are  the  events  of  domestic 
life,  which  instead  of  assimilating  tempers  tend  to  accentuate  slight 
differences  in  them.  Thus  if  some  members  of  a  family  are  a  little 
submissive  by  nature,  others  who  are  naturally  domineering  are 
tempted  to  become  more  so.  Then  the  acquired  habit  of  dictation 
in  these  reacts  upon  the  others  and  makes  them  still  more  sub- 
missive. In  the  collection  I  made  of  the  histories  of  twins  who 
were  closely  alike,  it  was  most  commonly  said  that  one  of  the  twins 
was  guided  by  the  other.  I  suppose  that  after  their  many  childish 
struggles  for  supremacy,  each  finally  discovered  his  own  relative 
strength  of  character,  and  thenceforth  the  stronger  developed  into 
the  leader,  while  the  weaker  contentedly  subsided  into  the  position 
of  being  led.  Again,  it  is  sometimes  observed  that  one  member  of 
an  otherwise  easygoing  family,  discovers  that  he  or  she  may  exer- 
cise considerable  power  by  adopting  the  habit  of  being  persistently 
disagreeable  whenever  he  or  she  does  not  get  the  first  and  best  of 
everything.  Some  wives  contrive  to  tyrannise  over  husbands  who 
are  mild  and  sensitive,  who  hate  family  scenes  and  dread  the  dis- 
grace attending  them,  by  holding  themselves  in  readiness  to  fly 
into  a  passion  whenever  their  wishes  are  withstood.  They  thus 
acquire  a  habit  of  "  breaking  out,"  to  use  a  term  familiar  to  the 
warders  of  female  prisons  and  lunatic  asylums ;  and  though  their 
relatives  and  connections  would  describe  their  tempers  by  severe 
epithets,  yet  if  they  had  married  masterful  husbands  their  characters 
might  have  developed  more  favourably. 

To  recapitulate  briefly,  one  set  of  influences  tends  to  mix  good 
and  bad  tempers  in  a  family  at  haphazard ;  another  set  tends  to 
assimilate  them,  so  that  they  shall  all  be  good  or  all  be  bad ;  a 
third  set  tends  to  divide  each  family  into  contrasted  portions. 
We  have  now  to  ascertain  the  facts  and  learn  the  results  of  these 
opposing  influences. 

In  dealing  with  the  distribution  of  temper  in  Fraternities,^  we 

^  A  Fraternity  consists  of  the  brothers  of  a  family,  and  of  the  sisters  after  the 
qualities  of  the  latter  have  been  transmuted  to  their  Male  Equivalents  ;  but  as 
no  change  in  the  Female  values  seems  really  needed,  so  none  has  been  made  in 
respect  to  Temper. 


APPENDIX  D. 


235 


can  only  make  use  of  those  in  which  at  least  two  cases  of  temper 
are  recorded  ;  they  are  146  in  number.  I  have  removed  all  the 
cases  of  neutral  temper,  treating  them  as  if  they  were  non-existent, 
and  dealing  only  with  the  remainder  that  are  good  or  bad.  We 
have  next  to  eliminate  the  haphazard  element.  Beginning  with 
Fraternities  of  two  persons-  only,  either  of  whom  is  just  as  likely  to 
be  good  as  bad  tempered,  there  are,  as  we  have  already  seen,  four 
possible  combinations,  resulting  in  the  proportions  of  1  case  of  both 
good,  2  cases  one  good  and  one  bad,  and  one  case  of  both  bad.  I 
have  42  such  Fraternities,  and  the  observed  facts  are  that  in  10 
of  them  both  are  good  tempered,  in  20  one  is  good  and  one  bad, 
and  in  12  both  are  bad  tempered.  Here  only  a  trifling  and  un- 
trustworthy difference  is  found  between  the  observed  and  the 
haphazard  distribution,  the  other  conditions  having  neutralised 
each  other.  But  when  we  proceed  to  larger  Fraternities  the  test 
becomes  shrewder,  and  the  trifling  difference  already  observed 
becomes  more  marked,  and  is  at  length  unmistakable.  Thus  the 
successive  lines  of  Table  III.  show  a  continually  increasing  diverg- 
ence between  the  observed  and  the  haphazard  distribution  of 
temper,  as  the  Fraternities  increase  in  size.     A  compendious  com- 


TABLE  3. 

DlSTEIBTJTION   OF    TeMPEE   IN    FeATERNITIES. 


A. — Observed. 

B. — Haphazard. 

Number 

in  each 

Fraternity. 

Numl>er 
of  Fra- 
ternities. 

All 
good- 
tem- 
pers. 

Intermediate 
cases. 

All 

bad- 

tem- 

"  pers. 

All 
good- 
tem- 
pers. 

Intermediate 
cases. 

All 
bad- 
tem- 
pers. 

2 
3 
4 
5 
6 

42 
55 
29 
6 
14 

10 

11 

5 

1 

1 

20 

15          21 

6        9        8 

0      2       10 

0     13      3     2 

12 
8 
1 
2 
4 

10 

7 
2 
0 
0 

21 

20         21 

8       12       8 

12       2      1 

2     4      5      4     2 

11 

7 
2 
0 
0 

4  to  6 

49 

7 

7 

2 

2 

236  NATUR.VL  INHERITANCE. 

parison  is  made  in  the  bottom  line  of  the  Table  by  adding  together 
the  instances  in  which  the  Fraternities  are  from  4  to  6  in  number, 
and  in  taking  only  those  in  which  all  the  members  of  the  Fraternity 
were  alike  in  temper,  whether  good  or  bad.  There  are  7  +  7,  or  14, 
observed  cases  of  this  against  2  +  2,  or  4,  haphazard  cases,  found  in 
a  total  of  49  Fraternities.  Hence  it  follows  that  the  domestic  influ- 
ences that  tend  to  differentiate  temper  wholly  fail  to  overcome  the 
influences,  hereditary  and  other,  that  tend  to  make  it  uniform  in 
the  same  Fraternity. 

As  regards  direct  evidences  of  heredity  of  temper,  we  must  frame 
our  inquiries  under  a  just  sense  of  the  sort  of  materials  we  have  to 
depend  upon.  They  are  but  coarse  portraits  scored  with  white  or 
black,  and  sorted  into  two  heaps,  irrespective  of  the  gradations  of 
tint  in  the  originals.  The  processes  I  have  used  in  discussing  the 
heredity  of  stature,  eye-colour,  and  artistic  faculty,  cannot  be 
employed  in  dealing  with  the  heredity  of  temper.  I  must  now 
renounce  those  refined  operations  and  set  to  work  with  ruder  tools 
on  my  rough  material. 

The  first  inquiry  will  be.  Do  good-tempered  parents  have,  on  the 
whole,  good-tempered  children,  and  do  bad-tempered  parents  have 
bad-tempered  ones?  I  have  43  cases  where  both  parents  are 
recorded  as  good-tempered,  and  25  where  they  were  both  bad- 
tempered.  Out  of  the  children  of  the  former,  30  per  cent,  were 
good-tempered  and  10  per  cent,  bad;  out  of  the  latter,  4  per  cent, 
were  good  and  52  per  cent,  bad-tempered.  This  is  emphatic  testi- 
mony to  the  heredity  of  temper,  I  have  worked  out  the  other  less 
contrasted  combinations  of  parental  temper,  but  the  results  are 
hardly  worth  giving.  There  is  also-  much  variability  in  the 
proportions  of  the  neutral  cases. 

I  then  attempted,  with  still  more  success,  to  answer  the  converse 
question.  Do  good-tempered  Fraternities  have,  on  the  whole,  good- 
tempered  ancestors,  and  bad  tempered  Fraternities  bad-tempered 
ones  1  After  some  consideration  of  the  materials,  I  defined — rightly 
or  wrongly — a  good-tempered  Fraternity  as  one  in  which  at  le  itt 
two  members  were  good-tempered  and  none  were  bad,  and  a  bad- 
tempered  Fraternity  as  one  in  which  at  least  two  members  were 
bad-tempered,  whether  or  no  any  cases  of  good  temper  were  said  to 
be  associated  with  them.     Then,  as  regards  the  ancestors,  I  thought 


APPENDIX  D.  237 

by  far  the  most  trustworthy  group  was  that  which  consisted  of 
the  two  parents  and  of  the  uncles  and  aunts  on  both  sides.  I 
have  thus  46  good-tempered  Fraternities  with  an  aggregate  of  333 
parents,  uncles,  and  aunts  ;  and  71  bad-tempered,  with  638  parents, 
uncles,  and  aunts.  In  the  former  group,  26  per  cent,  were  good 
tempered  and  18  bad ;  in  the  latter  group,  18  were  good-tempered 
and  29  were  bad,  the  remainder  being  neutral.  These  results  are 
almost  the  exact  counterparts  of  one  another,  so  I  seem  to  have 
made  good  hits  in  framing  the  definitions.  More  briefly,  wo  mav 
say  that  when  the  Fraternity  is  good-tempered  as  above  defined, 
the  number  of  good-tempered  parents,  uncles,  and  aunts,  exceeds 
that  of  the  bad-tempered  in  the  proportion  of  3  to  2  ;  and  that 
when  the  Fraternity  is  bad-tempered,  the  proportions  are  exactly 
reversed. 

I  have  attempted  in  other  ways  to  work  out  the  statistics  of 
hereditary  tempers,  but  none  proved  to  be  of  sufficient  value  for 
publication.  I  can  trace  no  prepotency  of  one  sex  over  the  other 
in  transmitting  their  tempers  to  their  children.  I  find  clear 
indications  of  strains  of  bad  temper  clinging  to  families  for  three 
generations,  but  I  cannot  succeed  in  putting  them  into  a  numerical 
form. 

It  must  not  be  thought  that  I  have  wished  to  deal  with  temper 
as  if  it  were  an  unchangeable  characteristic,  or  to  assign  more 
trustworthiness  to  my  material  than  it  deserves.  Both  these 
views  have  been  discussed  ;  they  are  again  alluded  to  to  show 
that  they  are  not  dismissed  from  my  mind,  and  partly  to  give  the 
opportunity  of  adding  a  very  few  further  remarks. 

Persons  highly  respected  for  social  and  public  qualities  may  be 
well-known  to  their  relatives  as  having  sharp  tempers  under  strong 
but  insecure  control,  so  that  they  "  flare  up "  now  and  then.  I 
have  heard  the  remark  that  those  who  are  over- suave  in  ordinary 
demeanour  have  often  vile  tempers.  If  this  be  the  case — and  I 
have  some  evidence  of  its  truth — I  suppose  they  are  painfully 
conscious  of  their  infirmity,  and  through  habitual  endeavours  to 
subdue  it,  have  insensibly  acquired  an  exaggerated  suavity  at  the 
times  when  their  temper  is  unprovoked.  Illness,  too,  has  much 
influence  in  affecting  the  temper.  Thus  I  sometimes  come  across 
entries  to  the  effect   of,   "  not  naturally  ill-tempered,  but  peevish 


238  NATURAL  INHERITANCE. 

through  illness."   Overwork  and  worry  will  make  even  mild-tempered 
men  exceedingly  touchy  and  cross. 

The  accurate  discernment  and  designation  of  character  is  almost 
beyond  the  reach  of  any  one,  but,  on  the  other  hand,  a  rough  estimate 
and  a  fair  description  of  its  prominent  features  is  easily  obtainable ; 
and  it  seems  to  me  that  the  testimony  of  a  member  of  a  family 
who  has  seen  and  observed  a  person  in  his  unguarded  moments 
and  under  very  varied  circumstances  for  many  years,  is  a  verdict 
deserving  of  much  confidence.  I  shall  have  fulfilled  my  object  in 
writing  this  paper  if  it  leaves  a  clear  impression  of  the  great  range 
and  variety  of  temper  among  persons  of  both  sexes  in  the  upper 
and  middle  classes  of  English  society ;  of  its  disregard  in  Marriage 
Selection;  of  the  great  admixture  of  its  good  and  bad  varieties 
in  the  same  family ;  and  of  its  being,  nevertheless,  as  hereditary 
as  any  other  quality.  Also,  that  although  it  exerts  an  immense 
influence  for  good  or  ill  on  domestic  happiness,  it  seems  that  good 
temper  has  not  been  especially  looked  for,  nor  ill  temper  especially 
shunned,  as  it  ought  to  be  in  marriage- selection. 


E. 

THE    GEOMETRIC    MEAN,    IN    VITAL    AND    SOCIAL    STATISTICS.^ 

My  purpose  is  to  show  that  an  assumption  which  lies  at  the  basis 
of  the  well-known  law  of  "  Frequency  of  Error"  is  incorrect  when 
applied  to  many  groups  of  vital  and  social  phenomena,  although  that 
law  has  been  applied  to  them  by  statisticians  with  partial  success. 
Next,  I  will  point  out  the  correct  hypothesis  upon  which  a  Law  of 
Error  suitable  to  these  cases  ought  to  be  calculated  ;  and  subsequently 
I  will  communicate  a  memoir  by  Mr.  (now  Dr.)  Donald  Macalister, 
who,  at  my  suggestion,  has  mathematically  investigated  the  subject. 

The  assumption  to  which  I  refer  is,  that  errors  in  excess  or  in 
deficiency  of  the  truth  are  equally  probable  ;  or  conversely,  that  if  two 
fallible    measurements  have  been  made  of  the  same  object,   their 

^  Epprinted,  with  slight  revision,  from  the  Proceedings  of  the  Eoyal  Society, 
No.  198,  1879.  ^ 


APPENDIX  E.  239 

arithmetical  mean  is  more  likely  to  be  the  true  measurement  than 
any  other  quantity  that  can  be  named. 

This  assumption  cannot  be  justified  in  vital  phenomena.  For  ex- 
ample, suppose  we  endeavour  to  match  a  tint ;  Weber's  law,  in  its 
approximative  and  simplest  form,  of  Sensation  varying  as  the 
logarithm  of  the  Stimulus,  tells  us  that  a  series  of  tints,  in  which 
the  quantities  of  white  scattered  on  a  black  ground  are  as  1,  2,  4, 
8,  16,  32,  &c.,  will  appear  to  the  eye  to  be  separated  by  equal  in- 
tervals of  tint.  Therefore,  in  matching  a  grey  that  contains  8  por- 
tions of  white,  we  are  just  as  likely  to  err  by  selecting  one  that  has 
16  portions  as  one  that  has  4  portions.  In  the  first  case  there 
Would  be  an  error  in  excess,  of  8  units  of  absolute  tint ;  in  the 
second  there  would  be  an  error  in  deficiency,  of  4.  Therefore,  an 
error  of  the  same  magnitude  in  excess  or  in  deficiency  is  not  equally 
probable  in  the  judgment  of  tints  by  the  eye.  Conversely,  if  two 
persons,  who  are  equally  good  judges,  describe  their  impressions  of 
a  certain  tint,  and  one  says  that  it  contains  4  portions  of  white  and 
the  other  that  it  contains  16  poitions,  the  most  reasonable  conclu- 
sion is  that  it  really  contains  8  portions.  The  arithmetic  mean  of 
the  two  estimates  is  10,  which  is  not  the  most  probable  value ;  it 
is  the  geometric  mean  8,  (4  :  8  :  :  8  :  16),  which  is  the  most  probable. 

Precisely  the  same  condition  characterises  every  determination  by 
each  of  the  senses;  for  exa^mple,  in  judgiug  of  the  weight  of  bodies  or 
of  their  temperatures,  of  the  loudness  and  of  the  pitches  of  tones, 
and  of  estimates  of  lengths  and  distances  as  wholes.  Thus,  three 
rods  of  the  lengths  a,  b,  c,  when  taken  successiv^ely  in  the  hand, 
appear  to  dilf er  by  equal  intervals  when  a  :  h  :  :  b  :  c,  and  not  when 
a—b^b  -  G.  In  all  physiological  phenomena,  where  there  is  on  the 
one  hand  a  stimulus  and  on  the  other  a  response  to  that  stimulus 
Weber's  or  some  other  geometric  law  may  be  assumed  to  prevail 
in  other  words,  the  true  mean  is  geometric  rather  than  arithmetic. 

The  geometric  mean  appears  to  be  equally  applicable  to  the  ma- 
jority of  the  influences,  which,  combined  with  those  of  purely  vital 
phenomena,  give  rise  to  the  events  with  which  sociology  deals.  It  is 
difficult  to  find  terms  sufficiently  general  to  apply  to  the  varied  topics 
of  sociology,  but  there  are  two  categories  which  are  of  common  oc- 
currence in  which  the  geometric  mean  is  certainly  appropriate.  The 
one  is  increase,  as  exemplified  by  the  growth  of  population,  where  an 


240  NATURAL  INHERITANCE. 

already  large  nation  tends  to  receive  larger  accessions  than  a  small 
oDe  under  similar  circumstances,  or  when  a  capital  employed  in  a 
business  increases  in  proportion  to  its  size.  The  other  category  is 
the  influences  of  circumstances  or  of  "  milieux  "  as  they  are  often 
called,  such  as  a  period  of  plenty  in  which  a  larger  held  or  a  larger 
business  yields  a  greater  excess  over  its  mean  yield  than  a  smaller 
one.  Most  of  the  causes  of  those  differences  with  which  sociology  are 
concerned,  and  which  are  not  purely  vital  phenomena,  such  as  those 
previously  discussed,  may  be  classified  under  one  or  other  of  these 
two  categories,  or  under  such  as  are  in  principle  almost  the  same. 
In  short,  sociological  phenomena,  like  vital  phenomena  are,  as  a 
general  rule,  subject  to  the  condition  of  the  geometric  mean. 

The  ordinary  law  of  Frequency  of  Error,  based  on  the  arithmetic 
mean,  corresponds,  no  doubt,  sufficiently  well  with  the  observed  facts 
of  vital  and  social  phenomena,  to  be  very  serviceable  to  statisticians, 
but  it  is  far  from  satisfying  their  wants,  and  it  may  lead  to  absurdity 
when  applied  to  wide  deviations.  It  asserts  that  deviations  in  excess 
must  be  balanced  by  deviations  of  equal  magnitude  in  deficiency ; 
therefore,  if  the  former  be  greater  than  the  mean  itself,  the  latter 
must  be  less  than  zero,  that  is,  must  be  negative.  This  is  an  impossi- 
bility in  many  cases,  to  which  the  law  is  nevertheless  applied  by  sta- 
tisticians with  no  small  success,  so  long  as  they  are  content  to  confine 
its  application  within  a  narrow  range  of  deviation.  Thus,  in  respect 
of  Stature,  the  law  is  very  correct  in  respect  to  ordinary  measure- 
ments, although  it  asserts  that  the  existence  of  giants,  whose  height 
is  more  than  double  the  mean  height  of  their  race,  implies  the  possi- 
bility of  the  existence  of  dwarfs,  whose  stature  is  less  than  nothing 
at  all. 

It  is  therefore  an  object  not  only  of  theoretical  interest  but  of 
practical  use,  to  thoroughly  investigate  a  Law  of  Error,  based  on  the 
geometric  mean,  even  though  some  of  the  expected  results  may 
perhaps  be  apparent  at  first  sight.  With  this  view  I  placed  the  fore- 
going remarks  in  Mr.  Donald  Macalister's  hands,  who  contributed 
a  memoir  that  will  be  found  in  the  Froc.  Royal  Soc,  No.  198,  1879, 
following  my  own.  It  should  be  referred  to  by  such  mathematicians 
as  may  read  this  book. 


APPENDIX  F.  241 

F. 

PROBABLE   EXTINCTION   OF    FAMILIES.^ 

The  decay  of  the  families  of  men  who  occupied  conspicuous  posi- 
tions in  past  times  has  been  a  subject  of  frequent  remark,  and  has 
given  rise  to  various  conjectures.  It  is  not  only  the  families  of  men 
of  genius  or  those  of- the  aristocracy  who  tend  to  perish,  but  it  is 
those  of  all  with  whom  history  deals,  in  any  way,  even  such  men 
as  the  burgesses  of  towns,  concerning  whom  Mr.  Doubleday  has 
inquired  and  written.  The  instances  are  very  numerous  in  which 
surnames  that  were  once  common  have  since  become  scarce  or  have 
wholly  disappeared.  The  tendency  is  universal,  and,  in  explanation 
of  it,  the  conclusion  has  been  hastily  drawn  that  a  rise  in  physical 
comfort  and  intellectual  capacity  is  necessarily  accompanied  by 
diminution  in  "fertility" — using  that  phrase  in  its  widest  sense 
and  reckoning  abstinence  from  marriage  as  one  cause  of  sterility. 
If  that  conclusion  be  true,  our  population  is  chiefly  maintained 
through  the  "  proletariat,"  and  thus  a  large  element  of  degradation 
is  inseparably  connected  with  those  other  elements  which  tend  to 
ameliorate  the  race.  On  the  other  hand,  M.  Alphonse  de  Candolle 
has  directed  attention  to  the  fact  that,  by  the  ordinary  law  of 
chances,"  a  large  proportion  of  families  are  continually  dying  out, 
and  it  evidently  follows  that,  until  we  know  what  that  proportion  is, 
we  cannot  estimate  whether  any  observed  diminution  of  sur- 
names among  the  families  whose  history  we  can  trace,  is  or  is  not  a 
sign  of  their  diminished  "fertility."  I  give  extracts  from  M.  De 
Candolle' s  work  in  a  foot-note,^  and  may  add  that,  although  I  have 
not  hitherto  published  anything  on  the  matter,  I  took  considerable 
pains  some  years  ago  to   obtain  numerical  results  in  respect  to  this 

1  Reprinted,  with  slight  revision,  from  the  Journ.  Anthropol.  Inst.   1888. 

2  "  An  milieu  des  renseignements  precis  et  des  opinions  tres-sensees  de 
MM.  Benoiston  de  Chateaunenf,  Galton,  et  autres  statisticiens,  je  n'ai  pas  ren- 
contre la  reflexion  bien  importaiite  qu'ils  auraient  du  faire  de  I'extinction  inevitable 
des  nonis  de  famille.  Evidemment  tons  les  noms  doivent  s'eteindre  ....  Un 
matliematicien  pourrait  calculer  comment  la  reduction  des  noms  ou  titres  aurait 
lieu,  d'apres  la  probabilite  des  naissances  toutes  feminines  ou  toutes  masculines 
ou  melangees  et  la  probabilite  d'absence  de  naissances  dans  un  couple  quelconque," 
&c. — Alphoxse  de  Candolle,  Histoire  des  Sciences  et  des  Savants,  1873. 

R 


242  NATURAL  INHERITANCE. 

very  problem.  I  made  certain  very  simple  and  not  very  inaccurate 
suppositions  concerning  average  fertility,  and  I  worked  to  the 
nearest  integer,  starting  with  10,000  persons,  but  the  computation 
became  intolerably  tedious  after  a  few  steps,  and  I  had  to  abandon 
it.  The  Rev.  H.  W.  Watson  kindly,  at  my  request,  took  the  pro- 
blem in  hand,  and  his  results  form  the  subject  of  the  following 
paper.  They  do  not  give  what  can  properly  be  called  a  general 
solution,  but  they  do  give  certain  general  results.  They  show  (1) 
how  to  compute,  though  with  great  labour,  any  special  case ;  (2)  a 
remarkably  easy  way  of  computing  those  special  cases  in  which  the 
law  of  fertility  approximates  to  a  certain  specified  form;  and  (3) 
how  all  surnames  tend  to  disappear. 

The  form  in  which  I  originally  stated  the  problem  is  as  follows. 
I  purposely  limited  it  in  the  hope  that  its  solution  might  be  more 
practicable  if  unnecessary  generalities  were  excluded  : — 

A  large  nation,  of  whom  we  will  only  concern  ourselves  with  the 
adult  males,  N  in  number,  and  who  each  bear  separate  surnames, 
colonise  a  district.  Their  law  of  population  is  such  that,  in  each 
generation,  a^  per  cent,  of  the  adult  males  have  no  male  children 
who  reach  adult  life ;  a^  have  one  such  male  child ;  a^  have  two ; 
and  so  on  up  to  a^y  who  have  five.  Find  (1)  what  proportion  of  the 
surnames  will  have  become  extinct  after  r  generations ;  and  (2)  how 
many  instances  there  will  be  of  the  same  surname  being  held  by  m 
persons. 

Discussion  of  the  iwobhm  hy  the  Rev.  H.  W.  Watson,  D.Sc,  F.R.S., 
formerly  Fellow  of  Trinity  College,  Gamhridge. 

Suppose  that  at  any  instant  all  the  adult  males  of  a  large 
nation  have  different  surnames,  it  is  required  to  find  how  many  of 
these  surnames  will  have  disappeared  in  a  given  number  of  genera- 
tions upon  any  hypothesis,  to  be  determined  by  statistical  investiga- 
tions, of  the  law  of  male  population. 

Let,  therefore,  a^  be  the  percentage  of  males  in  any  generation 
who  have  no  sons  reaching  adult  life,  let  a^  be  the  percentage  that 
have  one  such  son,  «2  the  percentage  that  have  two,  and  so  on  up  to 
a^,  the  percentage  that  have  q  such  sons,  q  being  so  large  that  it  is 
not  worth  while  to  consider  the  chance  of  any  man  having  more 
than  q  adult  sons — our  first  hypothesis  will  be  that  the  numbers 


APPENDIX  F.  243 

a^,  a-^,  ^2'  6^^-?  remain  the  same  in  each  succeeding  generation. 
We  shall  also,  in  what  follows,  neglect  the  overlapping  of  genera- 
tions— that  is  to  say,  we  shall  treat  the  problem  as  if  all  the  sons  born 
to  any  man  in  any  generation  came  into  being  at  one  birth,  and  as 
if  every  man's  sons  were  born  and  died  at  the  same  time.  Of  course 
it  cannot  be  asserted  that  these  assumptions  are  correct.  Yery 
probably  accurate  statistics  would  discover  variations  in  the  values 
of  CTq,  a-^,  etc.,  as  the  nation  progressed  or  retrograded ;  but  it  is  not 
at  all  likely  that  this  variation  is  so  rapid  as  seriously  to  vitiate  any 
general  conclusions  arrived  at  on  the  assumption  of  the  values 
remaining  the  same  through  many  successive  generations.  It  is 
obvious  also  that  the  generations  must  overlap,  and  the  neglect  to 
take  account  of  this  fact  is  equivalent  to  saying,  that  at  any  given 
time  we  leave  out  of  consideration  those  male  descendants,  of  any 
original  ancestor  who  are  more  than  a  certain  average  number  of 
generations  removed  from  him,  and  compensate  for  this  by  giving 
credit  for  such  male  descendants,  not  yet  come  into  being,  as  are  not 
more  than  that  same  average  number  of  generations  removed  from 
the  original  ancestors. 

Let  then   -^,     —J-,    —-4-,  etc.,  up  to   -—^  be  denoted  by  the  sym- 
100     100     100  ^100  ^  ^ 

bols  i^Q,  t^,  t^j  etc.,  up  to  ^g,  in  other  words,  let  ^q,  t-^,  etc.,  be  the 
chances  in  the  first  and  each  succeeding  generation  of  any  individual 
man,  in  any  generation,  having  no  son,  one  son,  two  sons,  and  so  on, 
who  reach  adult  life.  Let  N  be  the  original  number  of  distinct  sur- 
names, and  let  ^m^  be  the  fraction  of  IST  which  indicates  the  number 
of  such  surnames  with  s  representatives  in  the  rth  generation. 

Now,  if  any  surname  have  p  representatives  in  any  generation,  it 
follows  from  the  ordinary  theory  of  chances  that  the  chance  of  that 
same  surname  having  s  representatives  in  the  next  succeeding  gene- 
ration is  the  coefficient  of  x^  in  the  expansion  of  the  multinomial 

(^0  -1-  t-^x  4-  t^x^  -i- ,  etc.  4-  t^x'^y 

Let  then  the  expression  t^  +  t-^x  -f  t^x'^  -f  etc.  -f  t^x*^  be  repre- 
sented by  the  symbol  T. 

Then  since,  by  the  assumption  already  made,  the  number  of  sur- 
names with  no  representative  in  the  r-lth  generation  is  ^.^m^  N,  the 

K  2 


244  NATURAL  INHERITANCE. 

number  with  one  representative  ^_;^m^.N,  the  number  with  two 
r.im.2.  N  and  so  on,  it  follows,  from  what  we  last  stated,  that  the 
number  of  surnames  with  s  representatives  in  the  rth  generation 
must  be  the  coefficient  of  x'  in  the  expression 

I  ^.imo  +  ,_imiT  +  ,.im2T2+  etc.  +,_iW,,_iT^'-i    |n 

If,  therefore,  the  coefficient  of  N  in  this  expression  be  denoted  by 
y^  (x)  it  follows  that  r-i^n-^^,  r-i^h  ^^^  ^^  ^^'  ^^®  ^^^  coefficients  of  x, 
x^  and  so  on,  in  the  expression y]._j^  {x). 

If,  therefore,  a  series  of  functions  be  found  such  that 

f^{x):=^tQ  +  t-^x+  etc.   +tqX'^  and/].  {x)=/,._-^  (f^o  +  ^i^  ®*^-  +^^^*) 

then  the  proportional  number  of  groups  of  surnames  with  s  represen- 
tatives in  the  rth  generation  will  be  the  coefficient  of  x^inf^  {x) 
and  the  actual  number  of  such  surnames  will  be  found  by  multiplying 
this  coefficient  by  N.  The  number  of  surnames  nonrepresented  or  be- 
come extinct  in  the  rth  generation  will  be  found  by  multiplying 
the  term  independent  of  x  in./^  (x)  by  the  number  N. 

The  determination,  therefore,  of  the  rapidity  of  extinction  of  sur- 
names, when  the  statistical  data,  t^,  t-^,  etc.,  are  given,  is  reduced  to 
the  mechanical,  but  generally  laborious  process  of  successive  substi- 
tution of  Iq  +  t-^x  4-  t.^x^  +  etc.,  for  x  in  successively  determined  values 
of  y,.  (x),  and  no  further  progress  can  be  made  with  the  problem  until 
these  statistical  data  are  fixed ;  the  following  illustrations  of  the  ap- 
plication of  our  formula  are,  however,  not  without  interest. 

(1)  The  very  simplest  case  by  which  the  formula  can  be  illustrated 
is  when  q  =  2  and  t^,  tj,  t^  are  each  equal  to  J. 

Here  f,  (x)  =  l±|±^/,(x)  =  I  j  1  +  ^  {l+x  +  x'^)+  \  l+x  +  x^)^J 

and  so  on. 

Making  the  successive  substitutions,  we  obtain 

_j.  ,  .      1    (  13     5a3     Qx^     2x     X  \ 

f-,  {x)=.—  { 1 \-—   -\ 1-—   1- 

''"^  ^     3(99999/ 

■^''^  ^     2187  2187  2187   2187   2187   2187  2187  2187*^  2l87 

fpi)=  -63183+  •08306a;  +  -10635x2+  •07804a;3+  ■0Qi89x^+  -05443^5+  .oi437a;6 
+  -01692:^7+  •01144a;8+  -00367x9+  -00104x10+  '00015x11+  -00005x^2 
+  -00001x13  +  -00000x1*  +  -00000x15  +  -OOOOOx^^ 


APPENDIX  F.  245 


and  the  constant  term  in./^  (x)  or  ^ttIq  is  therefore 
«.oiQQ   .  '08306   ,  -10635  ,  '07804  ,  '06489  ,  '05443   ,  '01437  ,  '01692  ,    '01144 

0  oioo  + + + + +   + + + 

3  9  27  81  243  729         2187  6561 

•00367     '00104-00015 
19683       59049     177147 

The  value  of  which  to  five  places  of  decimals  is  '67528. 

The  constant  terms,  therefore,  in  y^,  /^  up  to  /^  when  reduced  to 
decimals,  are  in  this  case  '33333,  '48148,  '57110.,  '64113,  and  -65628 
respectively.  That  is  to  say,  out  of  a  million  surnames  at  starting, 
there  have  disappeared  in  the  course  of  one,  two,  etc.,  up  to  five 
generations,  333333,  481480,  571100,  641130,  and  675280  re- 
spectively. 

The  disappearances  are  much  more  rapid  in  the  earlier  than  in  the 
later  generations.  Three  hundred  thousand  disappear  in  the  first 
generation,  one  hundred  and  fifty  thousand  more  in  the  second,  and 
so  on,  while  in  passing  from  the  fourth  to  the  fifth,  not  more  than 
thirty  thousand  surnames  disappear. 

All  this  time  the  male  population  remains  constant.  For  it  is 
evident  that  the  male  population  of  any  generation  is  to  be  found  by 
multiplying  that  of  the  preceding  generation,  by  ^^  +  2^2?  ^^^  ^^^^ 
quantity  is  in  the  present  case  equal  to  one. 

If  axes  Ox  and  Ot/  be  drawn,  and  equal  distances  along  Ox  repre- 
sent generations  from  starting,  while  two  distances  are  marked 
along  every  ordinate,  the  one  representing  the  total  male  population 
in  any  generation,  and  the  other  the  number  of  remaining  surnames 
in  that  generation,  of  the  two  curves  passing  through  the  extremities 
of  these  ordinates,  the  j^opulation  curve  w^ll,  in  this  case,  be  a  straight 
line  parallel  to  Ox,  while  the  surname  curve  will  intersect  the  popu- 
lation curve  on  the  axis  of  y,  will  proceed  always  convex  to  the  axis 
of  X,  and  will  have  the  positive  part  of  that  axis  for  an  asymptote. 

The  case  just  discussed  illustrates  the  use  to  be  made  of  the  general 
formula,  as  well  as  the  labour  of  successive  substitutions,  when  the 
expressions/^  (x)  does  not  follow  some  assigned  law.  The  calcula- 
tion may  be  infinitely  simplified  when  such  a  law  can  be  found ; 
especially  if  that  law  be  the  expansion  of  a  binomial,  and  only  the 
extinctions  are  required. 

For  example,  suppose  that  the  terms  of  the  expression  tQ  +  t-^x  + 
etc.  +  tgCCg  are  proportional    to  the  terms  of  the  expanded  binomial 


246  NATURAL  INHERITANCE. 

(a-\-hxY  i.e.   suppose  tliat   fr. —  „  t\=^Q ;—    and  so  on. 

Here/,  (^)=^ —  -,,      and  .m.  =  . — 

'^^  ^  ^       {a  +  by  ^    ^      {a  +  bf 

J-  /  \  1        /      ,  i{a  +  bxy\q 

f^  (^)  ^  1 7T    1    «  +  0^-7 TV-   \ 


2^/^o  "^  " ^  "^    ^ 


{a  +  bY\  '    M 

Generally  .m,  =  ^-1^^  {  «  +  5.,mo  }  ^  =  ^^^  {  ^  +  ..,m,  }  ^ 

If,  therefore,  we  wish  to  find  the  number   of  extinctions  in  any 
generation,  we  have  only  to   take  the  number  in  the   preceding 

generation,  add  it  to  the  constant  fraction  _  ,  raise  the  sum  to  the 

b 

power  of  q,  and  multiply  by 


{a-\-bY 

"With  the  aid  of  a  table  of  logarithms,  all  this  may  be  effected  for 
a  great  number  of  generations  in  a  very  few  minutes.  It  is  by  no 
means  unlikely  that  when  the  true  statistical  data  ifg,  t^^,  etc.,  t^  are 
ascertained,  values  of  a,  b,  and  q  may  be  found,  which  shall  render 
the  terms  of  the  expansion  (a  +  bxy  approximately  proportionate  to 
the  terms  of/  (x).  If  this  can  be  done,  we  may  ajjproximate  to 
the  determination  of  the  rapidity  of  extinction  with  very  great  ease, 
for  any  number  of  generations,  however  great. 

For  example,  it  does  not  seem  very   unlikely  that  the  value  of  q 

might  be  5,  while  t^,  t^...t^  might  be  '237,  '396,  264,  -088,  '014,  -001, 

or  nearly,  J,  J,  -^\,  -^j,  ^-i^,  and  jJ^o- 

(3  +  xY  3^ 

Should  that  be  the  case,  we  have,  /j  (x)  =  -^ ^    ^rriQ  =  _ 


and    generally  ^m^  =  75  ]    3  +  ^.-^ttiq    > 


45 


Thus  we  easily  get  for  the  number  of  extinctions  in  the  first  ten 
generations  respectively. 

•237,  -346,  -410,  -450,  -477,  -496,  -510,  -520,  -527,  -533. 

We  observe  the  same  law  noticed  above  in  the  case  of  — 

3 

viz.,  that  while  237  names  out  of  a  thousand  disappear  in  the  first 


APPENDIX  F.  247 

step,  and  an  additional  109  names  in  the  second  step,  there  are  only 
27  disappearances  in  the  fifth  step,  and  only  six  disappearances  in  the 
tenth  step. 

If  the  curves  of  surnames  and  of  population  were  drawn  from  this 
case,  the  former  would  resemble  the  corresponding  curve  in  the  case 
last  mentioned,  while  the  latter  would  be  a  curve  whose  distance 
from  the  axis  of  x  increased  indefinitely,  inasmuch  as  the  expression 

^1  +  2^2 +^^3  +  4^4  +  ^^5 

is  greater  than  one. 

"Whenever  /-^  (x)  can  be  represented  by  a  binomial,  as  above  sug- 
gested, we  get  the  equation 

whence  it  follows  that  as  r  increases  indefinitely  the  value  of  ^m^  ap- 
proaches indefinitely  to  the  value  ?/  where 


^=(^){''+^4 


that  is  where  y=l. 

All  the  surnames,  therefore,  tend  to  extinction  in  an  indefinite 
time,  and  this  result  might  have  been  anticipated  generally,  for  a  sur- 
name once  lost  can  never  be  recovered,  and  there  is  an  additional 
chance  of  loss  in  every  successive  generation.  This  result  must  not 
be  confounded  with  that  of  the  extinction  of  the  male  population ;  for 
in  every  binomial  case  where  q  is  greater  than  2,  we  have  t-^  +  21^  +  etc. 
-\-qt^>l,  and,  therefore  an  indefinite  increase  of  male  population. 


The  true  interpretation  is  that  each  of  the  quantities,  ^m^, 


Ml 


2' 

etc.,  tends  to  become  zero,  as  t  is  indefinitely  increased,  but  that  it 
does  not  follow  that  the  product  of  each  by  the  infinitely  large  num- 
ber N  is  also  zero. 

As,  therefore,  time  proceeds  indefinitely,  the  number  of  surnames 
extinguished  becomes  a  number  of  the  same  order  of  magnitude  as  the 
total  number  at  first  starting  in  N,  while  the  number  of  surnames 
represented  by  one,  two,  three,  etc.,  lepresentatives  is  some  infinitely 
smaller  but  finite  number.  "When  the  finite  numbers  are  multiplied 
by  the  corresponding  number  of  representatives,  sometimes  infinite  in 
number,  and  the  products  added  together,  the  sum  will  generally  ex- 
ceed the  original  number  N.  In  point  of  fact,  just  as  in  the  cases 
calculated  above  to  five  generations,  we  had  a  continual,  and  indeed 


248  NATURAL  INHERITANCE. 

at  first,  a  rapid  extinction  of  surnames,  combined  in  the  one  case 
with  a  stationary,  and  in  the  other  case  an  increasing  population,  so 
is  it  when  the  number  of  generations  is  increased  indefinitely.  We 
have  a  continual  extinction  of  surnames  going  on,  combined  with 
constancy,  or  increase  of  population,  as  the  case  may  be,  until  at 
length  the  number  of  surnames  remaining  is  absolutely  insensible,  as 
compared  with  the  number  at  starting ;  but  the  total  number  of 
representatives  of  those  remaining  surnames  is  infinitely  greater  than 
the  original  number. 

We  are  not  in  a  position  to  assert  from  actual  calculation  that  a 
corresponding  result  is  true  for  every  form  oif^  (x),  but  the  reason- 
able inference  is  that  such  is  the  case,  seeing  that  it  holds  whenever 

/j  (x)  may  be  compared  with  ^  y  whatever  a,  h,  or  q  may  be. 


G. 

ORDERLY  ARRANGEMENT  OF  HEREDITARY  DATA. 

There  are  many  methods  both  of  drawing  pedigrees  and  of 
describing  kinship,  but  for  my  own  purposes  I  still  prefer  those  that 
I  designed  myself.  The  chief  requirements  that  have  to  be  fulfilled 
are  compactness,  an  orderly  and  natural  arrangement,  and  clearly 
intelligible  symbols. 

Nomenclature.— A.  symbol  ought  to  be  suggestive,  consequently 
the  initial  letter  of  a  word  is  commonly  used  for  the  purpose.  But 
this  practice  would  lead  to  singular  complications  in  symbolizing 
the  various  ranks  of  kinship,  and  it  must  be  applied  sparingly.  The 
letter  F  is  equally  likely  to  suggest  any  one  of  the  three  very  diffe- 
rent words  of  Father,  Female,  and  Fraternal.  The  letter  M  suggests 
both  Mother  and  Male  ;  S  would  do  equally  for  Son  and  for  Sister. 
Whether  they  are  English,  French,  or  German  words,  much  the 
same  complexity  prevails.  The  system  employed  in  Hereditary 
Genius  had  the  merit  of  brevity,  but  was  apt  to  cause  mistake  ;  it 
was  awkward  in  manuscript  and  difficult  to  the  printer,  and  I  have 
now  abandoned  it  in  favour  of  the  method  employed  in  the  Records 


APPENDIX  G. 


249 


of  Family  Faculties,  This  will  now  be  briefly  described  again. 
Each  kinsman  can  be  described  in  two  ways,  either  by  letters  or  by 
a  number.  In  ordinary  cases  both  the  letter  and  number  are 
intended  to  be  used  simultaneously,  thus  FF.8.  means  the  Father's 
Father  of  the  person  described,  though  either  FF  or  8,  standing  by 
themselves,  would  have  the  same  meaning.  The  double  nomen- 
clature has  great  practical  advantages.  It  is  a  check  against  mis- 
take and  makes  reference  and  orderly  arrangement  easy. 

As  regards  the  letters,  F  stands  for  Father  and  M  for  Mother, 
whenever  no  letter  succeeds  them  ;  otherwise  they  stand  for  Father's 
and  for  Mother's  respectively.  Thus  F  is  Father ;  FM  is  Father's 
Mother ;  FMF  is  Father's  Mother's  Father. 

As  regards  the  principle  upon  which  the  numbers  are  assigned, 
arithmeticians  will  understand  me  when  I  say  that  it  is  in  accord- 
ance with  the  binary  system  of  notation,  which  runs  parallel  to  the 
binary  distribution  of  the  successive  ranks  of  ancestry,  as  two 
parents,  four  grandparents,  eight  great-grandparents,  and  so  on. 
The  ''  subject "  of  the  pedigree  is  of  generation  O ;  that  of  his 
parents,  of  generation  1';  that  of  his  grandparents,  of  generation  2,  &c. 
This  is  clearly  shown  in  the  following  table  : — 


Kinship. 

Order 
of 

Genera- 
tion. 

Numerical  Yalues 

in  Binary  Notation. 

in  Decimal  Nota- 
tion. 

Child 

0 

1 

1 

Parents 

1 

10 

11 

2  . 

3 

Gr.  Par. 

2 

100 

101 

110 

111 

4 

5 

6 

7 

G.  Gr.  Par.   ...... 

3      < 

1000 
1001 

1010 
1011 

1100 
1100 

1110 

1111 

8 
9 

10 
11 

12 
13 

14 
15 

All  the  male  ancestry  are  thus  described  by  even  numbers  and  the 
female  ancestry  by  odd  ones.     They  run  as  follows  : — 


250  NATURAL  INHERITANCE. 

E,2.  M,  3. 

FF,  4.  FM,  5.  MF,  6.  MM,  7. 

FFF,  8.  FMF,  10.  MFF,  12.  MMF,  14. 

FFM,  9.  FMM,  11.  MFM,  13.  MMM,  15. 

It  will  be  observed  that  the  double  of  the  number  of  any  ancestor 
is  that  of  his  or  her  Father ;  and  that  the  double  of  the  number 
2olus  1  is  that  of  his  or  her  Mother  ;  thus  FM  5  has  for  her  father 
FMF  10,  and  for  her  mother  FMM  11. 

When  the  word  Brother  or  Sister  has  to  be  abbreviated  it  is  safer 
not  to  be  too  stingy  in  assigning  letters,  but  to  write  hr,  sr,  and  in 
the  plural  hrs,  srs  ;  also  for  the  long  phrase  of  ''  brothers  and  sisters," 
to  write  hrss. 

All  these  symbols  are  brief  enough  to  save  a  great  deal  of  space, 
and  they  are  perfectly  explicit.  When  such  a  phrase  has  to  be 
expressed  as  "  the  Fraternity  of  whom  FF  is  one "  I  write  in  my 
own  notes  simply  FF',  but  there  has  been  no  occasion  to  adopt  this 
symbol  in  the  present  book. 

I  have  not  satisfied  myself  as  to  any  system  for  expressing 
descendants.  Theoretically,  the  above  binary  system  admits  of 
extension  by  the  use  of  negative  indices,  but  the  practical  applica- 
tion of  the  idea  seems  cumbrous. 

We  and  the  French  sadly  want  a  word  that  the  Germans  possess 
to  stand  for  Brothers  and  Sisters.  Fraternity  refers  properly  to  the 
brothers  only,  but  its  use  has  been  legitimately  extended  here  to 
mean  the  brothers  and  the  sisters,  after  the  qualities  of  the  latter 
have  been  reduced  to  their  male  equivalents.  The  Greek  word 
adelpliic  would  do  for  an  adjective. 

Pedigrees. — The  method  employed  in  the  Record  of  Family  Faculties 
for  entering  all  the  facts  concerning  each  kinsman  in  a  methodical 
manner  was  fully  described  in  that  book,  and  could  not  easily  be 
epitomised  here ;  but  a  description  of  the  method  in  which  the 
manuscript  extracts  from  the  records  have  been  made  for  my  own 
use  will  be  of  service  to  others  when  epitomising  their  own  family 
characteristics.  It  will  be  sufficient  to  describe  the  quarto  books 
that  contain  the  medical  extracts.  Each  page  is  ten  and  a  half  inches 
high  and  eight  and  a  half  wide,  and  the  two  pages,  252,  253,  that  are 


APPENDIX  G. 


251 


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252 


NATURAL  INHERITANCE. 


Example  A. 


Father's  name James  Gladding. 

Mother's  maiden  name   ....  Maey  Claeemont. 

Initials. 
J.  G. 

R.  G- 
W.  G. 
F.  L. 
C.  G. 

M.  G. 

A.  C. 
W.  C. 

E.  C. 

F.  R. 
R.N. 
L.  C. 

Kin. 

Principal  illnesses  and  cause  of  death. 

Age  at 
death. 

Father 

Bad  rheum,  fever  ;  agonising   headaches ;  diar- 
rhoea ;  bronchitis  ;  pleurisy .    .  Heart  disease 

54 

56 
83 
73 

63 

46 
62 
19 
85 
50 
21 

bro. 
bro. 
sis. 
sis. 

Rheum,  gout Apoplexy 

Good  health  except  gout ;  paralysis  later  Apoplexy 
Rheum,  fever  and  rheum,  gout    .    .    .  Apoplexy 
Delicate (inoculated)  Small  pox 

Mother 

Tendency  to  lung   disease  ;    biliousness  ;    fre- 
quent heart  attacks  .  Heart  disease  and  dropsy 

bro. 
bro. 
bro. 

sis. 
sis. 
sis. 

Good  health     .           Accident 

Led  a  wild  life Premature  old  age 

Always  delicate Consumption 

Small-pox  three  times   ....    General  failure 

Bilious  ;  weak  health Cancer 

Fever 

M.  G. 
K.  G. 
G.  L. 

F.  S. 
R.  F. 
L.  G. 

bro. 
bro. 

sis. 

sis. 
sis. 

sis. 

Inflam.  lungs ;  rheum,  fever    .    .   Heart  disease 
Debility  ;  heart  disease  ;  colds     .    Consumption 
Bai  headaches  ;  coughs  ;  weak  spine  ;  hysteria  ; 

apoplexy Paralysis 

Bad  colds  ;  inflam.  lungs  ;  hysteria 

Infantile  paralysis  ;  colds  ;  nervous  depression  . 
Inflam.   brain,  also  lungs  ;  neuralgia  ;  nervous 

fever 

17 
40 

50 
living 
living 

living 

(Space  left  for  remarks.) 

APPENDIX  G. 


253 


Example  B. 


Fatlier's  name Julius  Fitzeoy. 

Mother's  maiden  name  .    .    .  Amelia  Mereyweathee. 


Initials. 


R.  F. 


L.  F.i 
A.  G.  F. 
W.  F. 


P.  M. 
A.  M. 

N.  M. 
R.  B. 
C.  M. 
F.  L. 


Kin. 


Father 


bro. 
hro. 
bro. 


Mother 


bro. 
bro. 
bro, 

sis.  • 

sis. 

sis. 


Principal  illnesses  and  cause  of  death. 


Gouty  Habit  .    .  Weak  Heart  and  Congest.  Liver 


Gout  and  Decay 
.  .  .  .  Accideiit 
.    .    .   .  Typhoid 


Gall  stones 


Internal  Malady  (?)  Cancer 


Still  living. 


Paralysis 
Paralysis 


1  died  an  infant. 


.    .  Consumption 
PJieum.  in  Head 
Softening  of  Brain 


Age  at 
death. 


73 


48 
16 


55 

86 
85 

33 

88 
76 


G. 

F. 

H. 

F. 

S. 

T.  F. 

H. 

G. 

H. 

B.R. 

N. 

F. 

E. 

L.  F. 

bro. 

bro. 

bro. 

sis. 
sis. 
sis. 
sis. 


Gout :  tendency  to  mesenteric  disease  ;  eruptive 

disorders    .    .    ,     Blood  poisoning  after  a  cut 

Liver  deranged  ;  bad  headaches  ;  once  supposed 

consumptive Gradual  Paralysis 

Eruptive  disorder ;  mesentery  disease  ;    inflam- 
mation of  liver    .    .    Inflamrtiation  of  Lungs 
Eruptive  disorder  ;  liver  .    .    .  Infiam.  of  Lungs 
Delicate  ;  tend,  to  mesent.  disease  ,  Consumption 

Colds  ;  liver  disorder Consumpition 

Mesenteric  disease  ;  grandular  swellings  .  Atrophy 
2  died  infants. 


46 

45 

42 
47 
29 
30 
16 


(Space  left  for  remarks.) 


254  NATURAL  INHERITANCE. 

found  wherever  the  book  is  opened,  relate  to  the  same  family.  The 
open  book  is  ruled  so  as  to  resemble  the  accompanying  schedule, 
which  is  drawn  on  a  reduced  scale  on  page  251.  The  printing  within 
the  compartments  of  the  schedule  does  not  appear  in  the  MS.  books, 
it  is  inserted  here  merely  to  show  to  whom  each  compartment  refers. 
It  will  be  seen  that  the  paternal  ancestry  are  described  in  the  left 
page,  the  maternal  in  the  right.  The  method  of  arrangement  is 
quite  orderly,  but  not  altogether  uniform.  To  avoid  an  unpleasing 
arrangement  like  a  tree  with  branches,  and  which  is  very  wasteful 
of  space,  each  grandparent  and  his  own  two  parents  are  arranged  in 
a  set  of  three  compartments  one  above  the  other.  There  are,  of 
course,  four  grandparents  and  therefore  four  such  sets  in  the 
schedule.  Reference  to  the  examples  A  andB  pages  252  and  253  will 
show  how  these  compartments  are  filled  up.  The  rest  of  the  Schedule 
explains  itself.  The  children  of  the  pedigree  are  written  below 
the  compartment  assigned  to  the  mother  and  her  brothers  and 
sisters ;  the  spare  spaces  are  of  much  occasional  service,  to  receive 
the  overfi.ow  from  some  of  the  already  filled  compartments  as  well 
as  for  notes.  It  is  astonishing  how  much  can  be  got  into  such  a 
schedule  by  writing  on  ruled  paper  with  the  lines  one-sixth  of  an 
inch  apart,  which  is  not  too  close  for  use.  Of  course  the  writing 
must  be  small,  but  it  may  be  bold,  and  the  figures  should  be  written 
very  distinctly. 

For  a  less  ambitious  attempt,  including  the  grandparents  and 
their  fraternity,  but  not  going  further  back,  the  left-hand  page 
would  sufiice,  placing  "  Children "  where  "  Father  "  now  stands, 
"Father's  Father"  for  "Father,"  and  so  on  throughout. 


INDEX. 


INDEX. 


Accidents,  19,  55,  65 

Acquired  peculiarities,  inheritance  of, 
14 

Album  for  Life  History,  220 

Ancestral  contributions,  134 

Adelphic,  250 

Aiitliropometric  Committee  of  the 
British  Assoc,  95  ;  anthrop.  labo- 
ratory data,  43,  46,  79 

Apparatus,  see  Models 

Acquired  faculties,  transmission  of,  16, 
197 

Artistic  Faculty,  154 

Averages  tell  little,  36  ;  comparison  of 
with  medians,  41 

Awards  for  E.F.F.,  75 


Bartholomew's  Hospital,  47 

Bias,  Statistical  effect  of,  in  marriage 
selection,  162  ;  in  suppressing  cause 
of  death,  168 

Blends,  or  refusals  to  blend,  12  ;  in 
issue  of  unlike  parents,  89  ;  in  hazel 
eyes,  145  ;  in  diseases,  169  ;  in  new 
varieties,  198  ;  in  temper,  233  ;  have 
no  effect  on  statistical  results,  17 


Cabs,  26,  30,  31 

Candolle,  A  de,  142,  145,  241  n 

Cards,  illustration  by,  188 

Chance,  19 

Chaos,  order  in,  66 

Child,  its  relation  to  mother,  15  ;  to 
either  parent,  19;  of  drunken  mother, 
15  ;  of  consumptive  mother,  177 

Cloud  compared  to  a  population,  164 

Co-Fraternities,  94 

Consumption,  171  ;  consumptivity,  181 


Contributions  from  separate  ancestors, 
134 

Cookery,  typical  dishes,  24 

Cousins,  their  nearness  in  kinship,  133  ; 
marriages  between,  175 

Crelle's  tables,  7 

Crowds,  characteristic  forms,  23 

Curve  of  Frequency,  40,  49  ;  of  Dis- 
tribution, 40,  54 


Darwin,  4,  19 

Data,  71 

De  Candolle,  142,  145,  241  n 

Deviations,  schemes  of,  51,  60  ;  cause 
of,  55.     See  Error. 

Dickson,  J.  D.  H.,  69,  102,  115,  Ap- 
pendix B.,  221 

Disease,  164;  skipping  a  generation, 
12 

Distribution,  schemes  of,  37  ;  normal 
curve  of,  54 


Error,  curve  of  Frequency,  49  ;  law  of, 

55  ;  probable,  57 
Evolution  not  by  minute  steps  only,  32 
Eye  coloue.,  138 


Families,  extinction  of,  Ajipendix  F., 

241 
Family  Records,  see  Records 
Father,  see  Parent 
Files  in  a  squadron,  111 
Filial  relation,  19  ;  regression,  95 
Fraternities,  meaning  of  word,  94,  234  ; 
to   be   treated  as  units,   35  ;  issued 
from  unlike  parents,  90  ;  variability 
in,  124,  129  ;  regression  in,  108 

S 


258 


INDEX. 


Frequency,  Scheme  of,  49  ;  model,  63 
surface  of,  102 


Museums  to  illustrate  evolution,  33 
Music,  155,  158 


Geometric  Mean,  118,  Appendix  E,  238 
Gouffe,  cookery  book,  24 
Governments,  22 
Grades,    37,    40  ;    of   modulus,    mean 

error,  &c.,  57 
Grove  battery,  31 


Natural,  its  meaning,  4  ;  natural  selec- 
tion, 32,  119 
Nephews,  133 
Nile  expedition,  23 
Nomenclature  of  kinship,  248 

NOEMAL  YARI ABILITY,  51 


Hazel  eyes,  144 

Hospital,  St.  Bartholomew's,  47 

Humphreys,  G.,  186 


Incomes  of  the  Euglish,  35 
Infertility  of  mixed  types,  31 
Insurance  companies,  185 
Inventions,  25 
Island  and  islets,  10 


Kenilworth  Castle,  21 
Kinship,    formula    of,    114 ;    table   of 
nearness  in  different  degrees,  132 


Laboratory,  anthropometric,  43,  46,  79 
Landscape,  characteristic  features,  23 
Latent  Elements,  187  ;   characters, 
11 


M,  its  signification,  41 

Macalister,  D.,  238 

McKendrick,  Professor,  20 

Malformation,  176 

Marriage  selection,  in  temper,  85,  232  ; 
in  eye-colour,  86,  147  ;  in  stature, 
87  ;  in  artistic  faculty,  157 

Means,  41  ;  mean  error,  57 

Mechanical  inventions,  25 

Median,  41 

Medical  students,  47 

Merrifield,  F.,  136 

Mid,  41  ;  Mid-parent,  87  ;  mid-popula- 
tion, 92  ;  mid-fraternity,  124  ;  mid- 
error,  58 

Models,  to  illustrate  Stability,  27  ; 
Curve  of  Frequency,  63  ;  Forecast  of 
stature  of  children,  107  ;  Surface  of 
Frequency,  115 

Modulus,  its  grade,  57 

Moths,  pedigree,  136 

Mother's  relation  to  her  child,  1 5  ;  in 
consumption,  177.     See  Parent 

Mulatto  blends,  13 


O'Brien,  84 
Omnibuses,  26,  32 
Order  in  apparent  chaos,  Q'd 
OEaANic  Stability,  4 


Paget,  Sir  J.,  47 

Palmer,  48 

Pangenesis,  19,  193 

Parents,  unlike  in  stature,  issue  of,  88  ; 
indirect  relation  to  children,  19  ; 
parental  relation,  110,  132 

Particulate  inheritance,  7 

Peas,  experiments  with,  79,  225 

Peculiarities,  natural  and  acquired,  4  ; 
inheritance  of,  138  ;  definition,  138, 
194 

Pedigree  moths,  136 

Pedigrees,  arrangement  of,  see  Appen- 
dix G.,  248,  250 

Percentiles,  46 

Personal  elements,  187  ;  in  incipient 
structure,  9 

Petty  influences,  16 

Population  to  be  treated  as  units,  35  ; 
their  mid-stature,  92  ;  their  Q,  93  : 
successive  generations  of,  115  ;  com- 
pared to  a  cloud,  164 

Priestley,  Dr.  W,  O.,  15 

Probability  integral,  54  ;  tables,  202  to 
205 

Probable  error,  53,  57 

Problems  in  the  law  of  error,  66 

Processes  in  Heredity,  4 

Pure  Breed,  189 


Q,  its  meaning,  53,  59 


R.  F.F.,  see  Records  of  Family  Faculties 
Rank  of  Faculty,  36,  46  ;  in  a  squadron, 

110 
Records  of  Family  Faculties,  data,  72  ; 
arrangement  of,    250  ;    prefaced   re- 
marks,  168  ;    object   of  book,  220  ; 
trustworthiness  of,  130,  167,  231 


INDEX. 


259 


Regression,  filial,  95,  98,  131  ;  mid- 
parental,  99,  101  ;  parental,  100 ; 
fraternal,  109  ;  generally,  103,  110, 
114  ;  is  a  measure  of  nearness  of 
kinship,  132  ;  in  artistic  faculty,  158; 
in  consuniptivity,  181  ;  an  element 
of  stability  in  characteristics  of  a 
people,  163 


Schemes  of  Distribution  and  Fre- 
quency, 35 

Scientific  societies,  their  government, 
22 

Selection  in  marriage,  85,  157,  147  ; 
eff"ect  of  bias  in,  162  ;  Natural  Selec- 
tion, 32,  119 

Ships  of  war,  123 

Simplification  of  inquiries  into  heredity, 
191 

Solomon,  24 

Special  data,  78 

Sports,  stability  of,  30,  198 

Squadron,  110 

Stable  forms,  20,  123,  198  ;  subordi- 
nate, 25 

Stability  of  sports,  30,  234  ;  of  charac- 
teristics in  a  people,  163 


Statistics,  are  processes  of  blending,  1 7  ; 

charms  of,  62 
Stature,  discussion  oe  Data,  83 
Strength,  Scheme  of,  37 
Structure,  incipient,  18 
Sweet  peas,  79,  225 
Swiss  guides,  23 

Temper,  Appendix  D.,  236,  85 

Traits,  9 

Transmutation  of  female  measures,  5, 

42,  78 
Trustworthiness  of  the  data,  130,  167, 

231 
Types,  24  ;  a  marked  family  type,  234 

Uncles,  133,  191 

Variability  of  Stature,  in  population, 
93  ;  in  Mid-Parents,  93  ;  in  Co-Fra- 
ternities, 94  ;  in  Fraternities,  124  ; 
in  a  pure  breed,  189 

Yariation,  individual,  9 

Watson,  Rev.  H.  W.,  242 
AVeissman,  193 


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